Vibration of axially loaded structures

Vibration of Axially Loaded Structures

Volumn , Issue , 2007, Pages 1-359

  Virgin, Lawrence N ^a  

^a Duke University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINED EFFECT; DYNAMIC BEHAVIORS; EXPERIMENTAL VERIFICATION; LOADED STRUCTURES; LOADING CONDITION; LOSS OF STABILITY; STRUCTURAL COMPONENT; STRUCTURAL MECHANICS;

EID: 84932601117     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511619236     Document Type: Book

References (552)

1. H. Goldstein. Classical Mechanics. Addison-Wesley, 1980.
2. E. T. Whittaker. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge Mathematical Library, 1988.
3. J. L. Synge and B. A. Griffith. Principles of Mechanics. McGraw-Hill, 1959.
4. I. Newton. Philosophiæ Naturalis Principia Mathematica. London, 1687.
5. L. Euler. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes. Marcum Michaelem Bousquet, 1744.
6. J. L. Lagrange. Mecanique Analytique. Courier, 1788.
7. L. Meirovitch. Principles and Techniques of Vibrations. Prentice Hall, 1997.
8. H. L. Langhaar. Energy Methods in Applied Mechanics. Wiley, 1962.
9. S. P. Timoshenko and J. M. Gere. Theory of Elastic Stability, 2nd ed. McGraw-Hill, 1961.
10. J. H. Argyris and S. Kelsey. Energy Theorems and Structural Analysis. Butterworth, 1960.
11. L. Meirovitch. Principles and Techniques of Vibrations. Prentice Hall, 1997.
12. W. T. Thomson. Theory of Vibration with Applications. Prentice Hall, 1981.
13. B. H. Tongue. Principles of Vibration. Oxford University Press, 1996.
14. J. P. den Hartog. Mechanical Vibrations. Dover, 1984.
15. R. Seydel. Practical Bifurcation and Stability Analysis. Springer, 1994.
16. D. J. Inman. Engineering Vibration. Prentice Hall, 2000.
17. S. G. Kelly. Fundamentals of Mechanical Vibrations. McGraw-Hill, 1993.
18. J. Guckenheimer and P. J. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.
19. V. I. Arnold. Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag, 1988.
20. S. H. Crandall. The role of damping in vibration theory. Journal of Sound and Vibration, 11: 3-18, 1970.
21. R. H. Abraham and C. D. Shaw. Dynamics: The Geometry of Behavior. Aerial Press, 1982.
22. J. M. T. Thompson. Instabilities and Catastrophes in Science and Engineering. Wiley, 1982.
23. D. W. Jordan and P. Smith. Nonlinear Ordinary Differential Equations. Oxford University Press, 1999.
24. A. H. Nayfeh and B. Balachandran. Applied Nonlinear Dynamics. Wiley, 1995.
25. Y. A. Mitropolskii. Problems of the Asymptotic Theory of Nonstationary Vibrations. Daniel Davey, 1965.
26. J. Kevorkian and J. D. Cole. Perturbation Methods in Applied Mathematics. Springer-Verlag, 1981.
27. O. Vallee and M. Soares. Airy Functions and Applications to Physics. World Scientific, 2004.
28. G. Temple and W. G. Bickley. Rayleigh's Principle and Its Applications to Engineering. Oxford University Press, 1933.
29. J. M. T. Thompson and G. W. Hunt. Elastic Instability Phenomena. Wiley, 1984.
30. H. L. Langhaar. Energy Methods in Applied Mechanics. Wiley, 1962.
31. G. Iooss and D. D. Joseph. Elementary Stability and Bifurcation Theory. Springer-Verlag, 1980.
32. M. Kubicek and M. Marek. Computational Methods in Bifurcation Theory and Dissipative Structures. Springer-Verlag, 1983.
33. M. Golubitsky and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory. Springer-Verlag, 1985.
34. K. Huseyin. Multiple Parameter Stability Theory and Its Applications. Oxford University Press, 1986.
35. H. Troger and A. Steindl. Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists. Springer-Verlag, 1991.
36. F. Bleich. Buckling Strength of Metal Structures. McGraw-Hill, 1952.
37. R. D. Cook. Concepts and Applications of Finite Element Analysis. Wiley, 1981.
38. L. N. Virgin. Parametric studies of the dynamic evolution through a fold. Journal of Sound and Vibration, 110: 99-109, 1986.
39. D. Hui and J. S. Hansen. The swallowtail and butterfly cuspoids and their application in the initial post-buckling of single-mode structural systems. Quarterly of Applied Mathematics, 38: 17-36, 1980.
40. L. N. Virgin and R. H. Plaut. Postbuckling and vibrations of linearly elastic and softening columns under self-weight. International Journal of Solids and Structures, 41: 4989-5001, 2004.
41. R. Thom. Structural Stability and Morphogenesis. Benjamin, 1975.
42. T. Poston and I. Stewart. Catastrophe Theory and Its Applications. Pitman, 1978.
43. R. H. Plaut and L. N. Virgin. Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. International Journal of Solids and Structures, 41: 4975-88, 2004.
44. D. J. Inman. Engineering Vibration. Prentice Hall, 2000.
45. L. Meirovitch. Principles and Techniques of Vibrations. Prentice Hall, 1997.
46. Y. G. Panovko and I. I. Gubanova. Stability and Oscillations of Elastic Systems-Paradoxes, Fallacies and New Concepts. Consultants Bureau, New York, 1965.
47. A. M. Lyapunov. The General Problem of the Stability of Motion. Princeton University Press, 1947.
48. A. P. Seyranian and A. A. Mailybaev. Multiparameter Stability Theory with Mechanical Applications. World Scientific, 2003.
49. K. Huseyin. Nonlinear Theory of Elastic Stability. Noordhoff, 1975.
50. H. H. E. Leipholz. Stability Theory. Wiley, 1987.
51. S. H. Strogatz. Nonlinear Dynamics and Chaos. Addison-Wesley, 1994.
52. E. H. Dowell. Aeroelasticity of Plates and Shells. Noordhoff, 1975.
53. MATLAB. User's guide. Technical report, The Math Works, 1989.
54. C. Hayashi. Nonlinear Oscillations in Physical Systems. Princeton University Press, 1964.
55. J. LaSalle and S. Lefschetz. Stability by Liapunov's Direct Method with Applications. Academic, 1961.
56. A. M. Lyapunov. Stability of Motion (Collected Papers). Academic, 1966.
57. K. Ogata. System Dynamics. Prentice Hall, 1998.
58. Lord Rayleigh (John William Strutt). The Theory of Sound. Dover, 1945.
59. B. H. Tongue. Principles of Vibration. Oxford University Press, 1996.
60. F. W. Williams and W. H. Wittrick. Exact buckling and frequency calculations surveyed. Journal of Structural Engineering, 109: 169-87, 1983.
61. R. Courant and D. Hilbert. Methods of Mathematical Physics. Wiley Classics Library, 1989.
62. E. H. Dowell and D. M. Tang. Dynamics of Very High Dimensional Systems. World Scientific, 2003.
63. J. H. Argyris and S. Kelsey. Energy Theorems and Structural Analysis. Butterworth, 1960.
64. G. Temple and W. G. Bickley. Rayleigh's Principle and Its Applications to Engineering. Oxford University Press, 1933.
65. W. J. Duncan. Galerkin's method in mechanics and differential equations. Reports and Memoranda No. 1798, Aeronautical Research Council London (England), 1937.
66. H. Troger and A. Steindl. Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists. Springer-Verlag, 1991.
67. H. B. Keller. Numerical solution of bifurcation and nonlinear eigenvalue problems. In P. Rabinowitz, editor, Applications of Bifurcation Theory. Academic Press, 1977, pp. 359-89.
68. T. J. R. Hughes. Finite Element Method-Linear Static and Dynamic Finite Element Analysis. Prentice Hall, 2000.
69. O. C. Zienkiewicz and R. L. Taylor. The Finite Element Method. McGraw Hill, 1989.
70. K. J. Bathe. Finite Element Procedures. Prentice Hall, 1995.
71. M. A. Crisfield. Nonlinear Finite Element Analysis of Solids and Structures, Vol. 1: Essentials. Wiley, 1997.
72. M. A. Crisfield. Nonlinear Finite Element Analysis of Solids and Structures, Vol. 2: Advanced Topics. Wiley, 1997.
73. J. M. T. Thompson and G. W. Hunt. AGeneral Theory of Elastic Stability. Wiley, 1973.
74. J. G. A. Croll and A. C. Walker. Elements of Structural Stability. Wiley, 1972.
75. G. J. Simitses. An Introduction to the Elastic Stability of Structures. Prentice Hall, 1976.
76. J. M. T. Thompson and G. W. Hunt. Elastic Instability Phenomena. Wiley, 1984.
77. L. N. Virgin. The dynamics of symmetric postbuckling. International Journal of Mechanical Sciences, 27: 235-48, 1985.
78. A. N. Kounadis. Nonlinear dynamic buckling of discrete dissipative or nondissipative systems under step loading. AIAA Journal, 29: 280-9, 1991.
79. A. N. Kounadis. Nonlinear dynamic buckling and stability of autonomous structural systems. International Journal of Mechanical Sciences, 35: 643-56, 1993.
80. I. Elishakoff, S. Marcus, and J. H. Starnes. On vibrational imperfection sensitivity of Augusti's model structure in the vicinity of a nonlinear static state. International Journal of Non-Linear Mechanics, 31: 229-36, 1996.
81. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in Fortran. Cambridge University Press, 1992.
82. A. C. Walker, J. G. A. Croll, and E. Wilson. Experimental models to illustrate the nonlinear behavior of elastic structures. Bulletin of Mechanical Engineering Education, 10: 247-59, 1971.
83. M. A. Souza. Vibration of thin-walled structures with asymmetric post-buckling characteristics. Thin-Walled Structures, 14: 45-57, 1992.
84. P. X. Bellini. The concept of snap-buckling illustrated by a simple model. International Journal of Nonlinear Mechanics, 7: 634-50, 1972.
85. D. A. Pecknold, J. Ghaboussi, and T. J. Healey. Snap-through and bifurcation in a simple structure. Journal of Engineering Mechanics (ASCE), 111: 909-22, 1985.
86. L. N. Virgin. Parametric studies of the dynamic evolution through a fold. Journal of Sound and Vibration, 110: 99-109, 1986.
87. J. M. T. Thompson and H. B. Stewart. Nonlinear Dynamics and Chaos, 2nd ed. Wiley, 2002.
88. G. Augusti, V. Sepe, and A. Paolone. An introduction to compound and coupled buckling and dynamic bifurcations. In J. Rondal, editor, Coupled Instabilities in Metal Structures: Theoretical and Design Aspects. Springer-Verlag, 1998, pp. 1-27.
89. N. Challamel. Softening branches of a two-degree-of-freedom system induced by spatial buckling. International Journal of Structural Stability and Dynamics, 6: 493-512, 2006.
90. L. N. Virgin and R. H. Plaut. Use of frequency data to predict secondary bifurcation. Journal of Sound and Vibration, 251: 919-26, 2002.
91. K. Huseyin and J. Roorda. The loading-frequency relationship in multiple eigenvalue problems. Journal of Applied Mechanics, 38: 1007-11, 1971.
92. K. Huseyin. Multiple Parameter Stability Theory and Its Applications. Oxford University Press, 1986.
93. R. H. Plaut. Column buckling when support stiffens under compression. Journal of Applied Mechanics, 56: 484, 1989.
94. R. H. Plaut. Stability and vibration of a column model with load-dependent support stiffness. Dynamics and Stability of Systems, 6: 79-88, 1991.
95. A. P. Seyranian and A. A. Mailybaev. Multiparameter Stability Theory with Mechanical Applications. World Scientific, 2003.
96. T. S. Parker and L. O. Chua. Practical Numerical Algorithms for Chaotic Systems. Springer-Verlag, 1989.
97. S. Wolfram. The Mathematica Book. Cambridge University Press, 1996.
98. MATLAB. User's guide. Technical report, The Math Works, 1989.
99. E. J. Doedel. AUTO-Software for continuation and bifurcation problems in ordinary differential equations. California Institute of Technology, 1986.
100. E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. J. Wang. Auto97: Continuation and bifurcation software for ordinary differential equations. Technical report, Department of Computer Science, Concordia University, Montreal, Canada, 1997 (available by FTP from ftp. cs. concordia. ca in directory pub/doedel/auto).
101. H. Chen. Nonlinear analysis of post-buckling dynamics and higher order instabilities of flexible structures. Ph. D. dissertation, Duke University, 2004.
102. R. Courant and D. Hilbert. Methods of Mathematical Physics. Wiley Classics Library, 1989.
103. L. Meirovitch. Principles and Techniques of Vibrations. Prentice Hall, 1997.
104. Lord Rayleigh (John William Strutt). The Theory of Sound. Dover, 1945.
105. H. M. Irvine and T. K. Caughey. The linear theory of free vibrations of a suspended cable. Proceedings of the Royal Society of London Series A, 341: 299-315, 1974.
106. S. Krenk. Mechanics and Analysis of Beams, Columns and Cables. Springer, 2001.
107. H. M. Irvine. Cable Structures. MIT Press, 1981.
108. S. E. Ramberg and O. M. Griffin. Free vibration of taut and slack marine cables. Journal of the Structural Division, Proc. ASCE, 103: 2079-92, 1977.
109. H. Lamb. Higher Mechanics. Cambridge University Press, 1929.
110. D. Yong. Strings, chains, and ropes. SIAM Review, 48: 771-81, 2006.
111. G. N. Watson. ATreatise on the Theory of Bessel Functions. Cambridge University Press, 1966.
112. H. Lamb. The Dynamical Theory of Sound. Arnold, 1910.
113. R. D. Blevins. Formulas for Natural Frequencies and Mode Shapes. Van Nostrand Rheinhold, 1979.
114. A. D. Dimarogonas. Vibration for Engineers. Prentice Hall, 1996.
115. A. Bokaian. Natural frequencies of beams under compressive axial loads. Journal of Sound and Vibration, 126: 49-65, 1988.
116. L. Meirovitch. Principles and Techniques of Vibrations. Prentice Hall, 1997.
117. J. M. T. Thompson and G. W. Hunt. Elastic Instability Phenomena. Wiley, 1984.
118. J. Szabo, Z. Gaspar, and T. Tarnai. Post-Buckling of Elastic Structures. Elsevier, 1986.
119. W. Nowacki. Dynamics of Elastic Systems. Chapman & Hall, 1963.
120. S. P. Timoshenko and D. H. Young. Elements of Strength of Materials. Van Nostrand Reinhold, 1977.
121. R. E. D. Bishop and W. G. Price. The vibration characteristics of a beam with an axial force. Journal of Sound and Vibration, 59: 237-44, 1978.
122. A. E. Galef. Bending frequencies of compressed beams. Journal of the Acoustical Society of America, 44: 643, 1968.
123. V. Birman, I. Elishakoff, and J. Singer. On the effect of axial compression on the bounds of simple harmonic motion. Israel Journal of Technology, 20: 254-8, 1982.
124. Z. P. Bazant and L. Cedolin. Stability of Structures. Oxford University Press, 1991.
125. D. Young and R. P. Felgar. Tables of characteristic functions representing normal modes of vibration of a beam. Technical report, The University of Texas, Publication No. 4913, 1949.
126. N. G. Stephen. Beam vibration under compressive axial load-upper and lower bound approximation. Journal of Sound and Vibration, 131: 345-50, 1989.
127. A. Bokaian. Natural frequencies of beams under tensile axial loads. Journal of Sound and Vibration, 142: 481-98, 1990.
128. G. J. Simitses. Dynamic Stability of Suddenly Loaded Structures. Springer-Verlag, 1989.
129. R. D. Blevins. Formulas for Natural Frequencies and Mode Shapes. Van Nostrand Rheinhold, 1979.
130. R. Courant and D. Hilbert. Methods of Mathematical Physics. Wiley Classics Library, 1989.
131. G. W. Housner and W. K. Tso. Dynamic behavior of supercritically loaded struts. ASCE Journal of Engineering Mechanics, 88: 41-65, 1962.
132. J. Roorda. The Instability of Imperfect Elastic Structures. Ph. D. dissertation, University of London, 1965.
133. R. Schmidt. Initial postbuckling of columns by the Rayleigh-Ritz method. Industrial Mathematics, 36: 67-76, 1986.
134. M. S. El Naschie. Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw-Hill, 1990.
135. S. M. Dickinson. The lateral vibration of slightly bent slender beams subject to prescribed axial end displacement. Journal of Sound and Vibration, 68: 507-14, 1980.
136. I. Elishakoff, V. Birman, and J. Singer. Influence of initial imperfections on nonlinear free vibrations of elastic bars. Acta Mechanica, 55: 191-202, 1985.
137. T. M. Atanackovic. Stability of a compressible elastic rod with imperfections. Acta Mechanica, 76: 203-22, 1989.
138. L. Tomski and S. Kukla. Free vibrations of a certain geometrically nonlinear system with initial imperfection. AIAA Journal, 28: 1240-5, 1989.
139. C. L. Dym. Stability Theory and Its Applications to Structural Mechanics. Noordhoff International, 1974.
140. S. P. Timoshenko and J. M. Gere. Theory of Elastic Stability, 2nd ed. McGraw-Hill, 1961.
141. H. G. Allen and P. S. Bulson. Background to Buckling. McGraw-Hill, 1980.
142. S. Woinowsky-Krieger. The effect of an axial force on the vibration of hinged bars. Journal of Applied Mechanics, 17: 35-36, March 1950.
143. F. J. Shaker. Effect of axial load on mode shapes and frequencies of beams. Technical report, NASA Lewis Research Center Report TN-8109, 1975.
144. W. J. Duncan. Galerkin's method in mechanics and differential equations. Reports and Memoranda No. 1798, 1937.
145. S. Karunamoorthy, D. A. Peters, and D. Barwey. Orthogonal polynomials for energy methods in rotary wing structural dynamics. Journal of the American Helicopter Society, 38: 93-8, 1993.
146. Y. R. Wang. The effect of wake dynamics on rotor eigenvalues in forward flight. Ph. D. dissertation, Georgia Institute of Technology, 1992.
147. A. R. S. Bramwell. Helicopter Dynamics. Arnold, 1976.
148. W. Johnson. Helicopter Theory. Princeton University Press, 1980.
149. V. T. Nagaraj. Relationship between fundamental natural frequency and maximum static deflection for rotating Timoshenko beams. Journal of Sound and Vibration, 201: 404-6, 1997.
150. C. L. Lee. Limit cycle measurements from a cantilever beam attached to a rotating body. AIAA Journal, 36: 1540-1, 1998.
151. C. D. Eick and M. P. Mignolet. Vibration and buckling of flexible rotating beams. AIAA Journal, 33: 528-38, 1995.
152. M. Behzad and A. R. Bastami. Effect of centrifugal force on natural frequency of lateral vibration of rotating shafts. Journal of Sound and Vibration, 274: 985-95, 2004.
153. R. V. Southwell and B. S. Gough. On the free transverse vibrations of airscrew blades. Technical Report 766, Rep. Mem. Aeronautical Research Council, 1921.
154. T. G. Carne, D. R. Martinez, and S. R. Ibrahim. Modal identification of rotating blade system. Technical report, AIAA-83-0815, 1983.
155. S. M. Hashemi, M. J. Richard, and G. Dhatt. A new dynamic finite element (dfe) formulation for lateral free vibrations of Euler-Bernoulli spinning beams using trigonomoetric shape functions. Journal of Sound and Vibration, 220: 601-24, 1999.
156. J. R. Banerjee. Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. Journal of Sound and Vibration, 233: 857-75, 2000.
157. S. Naguleswaran. Lateral vibration of a centrifugally tensioned uniform Euler-Bernoulli beam. Journal of Sound and Vibration, 176: 613-24, 1994.
158. G. H. Argyris and H-P. Mlejnek. Dynamics of Structures. North-Holland, 1991.
159. J. R. Banerjee, H. Su, and D. R. Jackson. Free vibration of rotating tapered beams using the dynamic stiffness method. Journal of Sound and Vibration, 298: 1034-54, 2006.
160. R. A. Ormiston and D. H. Hodges. Linear flap-lag dynamics of hingeless Helicopter rotor blades in hover. Journal of the American Helicopter Society, 17: 2-14, 1972.
161. D. H. Hodges and E. H. Dowell. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. Technical Report, NASA TN D-7818, 1974.
162. A. Bazoune. Survey on modal frequencies of centrifugally stiffened beams. Shock and Vibration Digest, 37: 449-69, 2005.
163. D. H. Hodges and R. A. Ormiston. Stability of elastic bending and torsion of uniform cantilevered rotor blades in hover. AIAA, 1973. Paper No. 73-405.
164. E. H. Dowell, J. Traybar, and D. H. Hodges. An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam. Journal of Sound and Vibration, 50: 533-44, 1977.
165. A. T. Frederick and I. Chopra. Assessment of transient analysis techniques for rotor stability testing. Journal of the American Helicopter Society, 35: 39-50, 1990.
166. C. E. Hammond. An application of Floquet theory to prediction of mechanical instability. Journal of the American Helicopter Society, 4: 14-23, 1974.
167. N. A. Cumpsty. Jet Propulsion. Cambridge University Press, 2003.
168. Y. C. Fan, M. S. Ju, and Y. G. Tsuei. Experimental study on vibration of a rotating blade. Journal of Engineering for Gas Turbines and Power, 116: 672-7, 1994.
169. R. G. Parker and C. D. Mote. Tuning of the natural frequency spectrum of a circular plate by in-plane stress. Journal of Sound and Vibration, 145: 95-110, 1991.
170. M. Beck. Die Knicklast des einseitig eingespannten, tangential gedruckten Stabes. Zeitschrift für Angewandte Mathematik und Physik, 3: 225-8, and 476-7, 1952.
171. H. Ziegler. Principles of Structural Stability. Blaidsell, 1968.
172. H. H. E. Leipholz. Stability Theory. Wiley, 1987.
173. C. Y. Wang. A critical review of the heavy elastica. International Journal of Mechanical Sciences, 28: 549-59, 1986.
174. L. N. Virgin. Free vibrations of imperfect cantilever bars under self-weight loading. Proceedings of the Institution of Mechanical Engineering, 201: 345-7, 1987.
175. A. G. Greenhill. Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and of the greatest height to which a tree of given proportions can grow. Proceedings of the Cambridge Philosophical Society, 4: 65-73, 1881.
176. A. G. Pugsley. Limits to size set by trees. The Structural Engineer, 66: 322-3, 1988.
177. D. F. Pilkington and J. B. Carr. Vibrations of beams subjected to end and axially distributed loading. Journal of Mechanical Engineering Science, 12: 70-2, 1970.
178. T. Huang and D. W. Dareing. Buckling and frequencies of long vertical pipes. Journal of the Engineering Mechanics Division, ASCE, 95: 167-81, 1969.
179. C. P. Sparks. Transverse modal vibrations of vertical tensioned risers: A simplified analytical approach. Oil and Gas Science and Technology, 57: 71-86, 2002.
180. D. J. Johns. Thermal Stress Analysis. Pergamon, 1965.
181. B. A. Boley and J. H. Weiner. Theory of Thermal Stresses. Wiley, 1960.
182. E. Sevin. On the elastic bending of columns due to dynamic axial forces including effects of axial inertia. Journal of Applied Mechanics, 27: 125-31, 1960.
183. H. Abramovich. Natural frequencies of Timoshenko beams under compressive axial loads. Journal of Sound and Vibration, 157: 183-9, 1992.
184. S. C. Chuang and J. T.-S. Wang. Vibration of axially loaded damped beams on viscoelastic foundation. Journal of Sound and Vibration, 148: 423-35, 1991.
185. H. L. Cox. Vibration of axially-loaded beams carrying distributed masses. Journal of the Acoustical Society of America, 30: 568-71, 1958.
186. M. Hetenyi. Beams on Elastic Foundation. University of Michigan Press, 1946.
187. R. H. Plaut and E. R. Johnson. The effect of initial thrust and elastic foundation on the vibration frequencies of a shallow arch. Journal of Sound and Vibration, 78: 565-71, 1981.
188. B. A. Boley and J. H. Weiner. Theory of Thermal Stresses. Wiley, 1960.
189. D. J. Johns. Thermal Stress Analysis. Pergamon, 1965.
190. N. Challamel, C. Lanos, and C. Casandjian. Localization in the buckling or in the vibration of a two-span weakened column. Engineering Structures, 28: 776-82, 2006.
191. C. L. Amba-Rao. Effect of end conditions on the lateral frequencies of uniform straight columns. Journal of the Acoustical Society of America, 42: 900-1, 1967.
192. M. Chi, B. G. Dennis, and J. Vossoughi. Transverse and torsional vibrations of an axially-loaded beam with elastically constrained ends. Journal of Sound and Vibration, 96: 235-41, 1984.
193. P. J. Wicks. Compound buckling of elastically supported struts. Journal of Engineering Mechanics, 113: 1861-69, 1987.
194. D. Zhou and Y. K. Cheung. The free vibration of a type of tapered beam. Computer Methods in Applied Mechanics and Engineering, 188: 203-16, 2000.
195. D. Zhou and Y. K. Cheung. Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions. Journal of Applied Mechanics, 68: 596-602, 2001.
196. M. Eisenberger. Buckling loads for variable cross section bars in a nonuniform thermal field. Mechanics Research Communications, 19: 259-66, 1992.
197. N. M. Auciello. On the transverse vibrations of non-uniform beams with axial loads and elastically restrained ends. International Journal of Mechanical Sciences, 43: 193-208, 2001.
198. J. Jaroszewicz and L. Zoryi. Investigation of the effect of axial loads on the transverse vibrations of a vertical cantilever with variable parameters. International Applied Mechanics, 36: 1242-51, 2000.
199. G. W. Housner and W. O. Keightley. Vibrations of linearly tapered cantilever beams. Journal of the Engineering Mechanics Division, ASCE, 88: 95-123, 1962.
200. R. P. Goel. Transverse vibration of tapered beams. Journal of Sound and Vibration, 47: 1-7, 1976.
201. F. W. Williams and J. R. Banerjee. Flexural vibrations of axially-loaded beams with linear or parabolic taper. Journal of Sound and Vibration, 99: 121-38, 1985.
202. L. N. Virgin. Free vibrations of imperfect cantilever bars under self-weight loading. Proceedings of the Institution of Mechanical Engineering, 201: 345-7, 1987.
203. A. G. Pugsley. Limits to size set by trees. The Structural Engineer, 66: 322-3, 1988.
204. R. H. Plaut, K. D. Murphy, and L. N. Virgin. Curve and surface veering for a braced column. Journal of Sound and Vibration, 187: 879-85, 1995.
205. W. J. Supple. Coupled branching configurations in the elastic buckling of symmetric structural systems. International Journal of Mechanical Sciences, 9: 97-112, 1967.
206. A. H. Chilver. Coupled modes of elastic buckling. Applied Mechanics Reviews, 15: 15-28, 1967.
207. E. P. Popov. Introduction to Mechanics of Solids. Prentice Hall, 1968.
208. S. P. Timoshenko and J. M. Gere. Theory of Elastic Stability, 2nd ed. McGraw-Hill, 1961.
209. T. M. Roberts. Natural frequencies of thin-walled bars of open cross-section. Journal of Engineering Mechanics, 113: 1584-93, 1987.
210. R. Parnes. Solid Mechanics in Engineering. Wiley, 2001.
211. H. W. Haslach and R. W. Armstrong. Deformable Bodies and Their Material Behavior. Wiley, 2004.
212. D. H. Hodges and E. H. Dowell. Non-linear equations of motion for elastic bending and torsion of twisted non-uniform rotor blades. Technical Report, NASA TN D-7818, 1974.
213. R. S. Barsoum and R. H. Gallagher. Finite element analysis of torsional and flexural-torsional stability problems. International Journal for Numerical Methods in Engineering, 2: 335-52, 1970.
214. W. F. Chen and E. M. Liu. Structural Stability: Theory and Implementation. Elsevier, 1987.
215. F. Mohri, L. Azrav, and M. Potier-Ferry. Vibration analysis of buckled thin-walled beams with open sections. Journal of Sound and Vibration, 275: 434-46, 2004.
216. S. P. Machado and V. H. Cortinez. Free vibration of thin-walled composite beams with static initial stresses and deformations. Engineering Structures, 29: 372-82, 2007.
217. J. M. T. Thompson and G. W. Hunt. Elastic Instability Phenomena. Wiley, 1984.
218. H. B. Harrison. Post-buckling behaviour of elastic circular arches, Part 2. Proceedings of the Institution of Civil Engineers, 65: 283-98, 1978.
219. N. J. Hoff. Buckling and stability: The forty-first Wilbur Wright memorial lecture. Journal of the Royal Aeronautical Society, 58: 3-52, 1954.
220. W. E. Gregory and R. H. Plaut. Dynamic stability boundaries for shallow arches. Journal of Engineering Mechanics, 108: 1036-50, 1982.
221. R. H. Plaut and L. N. Virgin. Use of frequency data to predict buckling. Journal of Engineering Mechanics, 116: 2330-5, 1990.
222. H. L. Schreyer and E. F. Masur. Buckling of shallow arches. Journal of Engineering Mechanics, ASCE, 92: 1-19, 1966.
223. L. W. Rehfield. Nonlinear flexural oscillations of shallow arches. AIAA Journal, 12: 91-3, 1974.
224. R. E. Fulton and F. W. Barton. Dynamic buckling of shallow arches. Journal of Engineering Mechanics, ASCE, 97: 865-77, 1971.
225. N. J. Hoff and V. G. Bruce. Dynamic analysis of the buckling of laterally loaded flat arches. Journal of Mathematical Physics, 32: 276-88, 1954.
226. A. M. Liapunov. Stability of Motion (Collected Papers). Academic, 1966.
227. D. L. C. Lo and E. F. Masur. Dynamic buckling of shallow arches. Journal of Engineering Mechanics, ASCE, 102: 901-17, 1976.
228. R. K. Livesley and D. B. Chandler. Stability Functions for Structural Frameworks. Manchester University Press, 1956.
229. M. R. Horne and W. Merchant. The Stability of Frames. Pergamon, 1965.
230. M. D. Capron and F. W. Williams. Exact dynamic stiffnesses for an axially loaded uniform Timoshenko member embedded in an elastic medium. Journal of Sound and Vibration, 124: 453-66, 1988.
231. J. Roorda and A. M. Chilver. Frame buckling: An illustration of the perturbation technique. International Journal of Non-linear Mechanics, 5: 235-46, 1970.
232. S. P. Timoshenko and D. H. Young. Elements of Strength of Materials. Van Nostrand Reinhold, 1977.
233. R. C. Hibbeler. Structural Analysis, 5th ed. Prentice Hall, 2002.
234. W. Nowacki. Dynamics of Elastic Systems. Chapman & Hall, 1963.
235. R. H. Gallagher. Finite Element Analysis: Fundamentals. Prentice Hall, 1975.
236. O. C. Zienkiewicz and R. L. Taylor. The Finite Element Method. McGraw-Hill, 1989.
237. A. Kassimali. Matrix Analysis of Structures. Brooks/Cole, 1999.
238. R. D. Cook. Concepts and Applications of Finite Element Analysis. Wiley, 1981.
239. K. J. Bathe. Finite Element Procedures. Prentice Hall, 1995.
240. B. A. Coulter and R. E. Miller. Vibration and buckling of beam columns subjected to non-uniform axial loads. International Journal of Numerical Methods, 23: 1739-55, 1986.
241. B. J. Hartz. Matrix formulation of structural stability problems. Journal of the Structural Division, ASCE, 91: 141-57, 1965.
242. R. W. Clough and J. Penzien. Dynamics of Structures. McGraw-Hill, 1982.
243. J. F. Doyle. Nonlinear Analysis of Thin-Walled Structures. Springer, 2001.
244. B. A. Ovunc. Effect of axial force on frameworks dynamics. Computers and Structures, 11: 389-95, 1980.
245. J. Przybylski, L. Tomski, and M. Golebiowska-Rozanow. Free vibration of an axially loaded prestressed planar frame. Journal of Sound and Vibration, 189: 609-24, 1996.
246. D. J. Mead. Free vibrations of self-strained assemblies of beams. Journal of Sound and Vibration, 249: 101-27, 2002.
247. M. I. Friswell and J. E. Mottershead. Finite-Element Model Updating in Structural Dynamics. Kluwer Academic, 1995.
248. N. A. J. Lieven and P. D. Greening. Effect of experimental pre-stress and residual stress on modal behavior. Philosophical Transactions of the Royal Society of London, 359: 97-111, 2001.
249. P. D. Greening and N. A. J. Lieven. Identification and updating of loading in frameworks using dynamic measurements. Journal of Sound and Vibration, 260: 101-15, 2003.
250. E. Riks. The application of Newton's method to the problem of elastic stability. Journal of Applied Mechanics, 39: 1060-6, 1972.
251. M. A. Crisfield. A fast incremental/iterative solution procedure that handles snapthrough. Computers and Structures, 13: 55-62, 1981.
252. R. Seydel. Practical Bifurcation and Stability Analysis. Springer, 1994.
253. I. Stanciulescu, L. N. Virgin, and T. A. Laursen. Finite element analysis of slender solar sail booms. Journal of Spacecraft and Rockets, 44: 528-37, 2007.
254. G. H. Argyris and H.-P. Mlejnek. Dynamics of Structures. North-Holland, 1991.
255. S. P. Timoshenko and S. Woinowsky-Krieger. Theory of Plates and Shells, 2nd ed. McGraw-Hill, 1968.
256. A. W. Leissa. Vibration of plates. Technical Report SP-160, NASA, 1969.
257. T. von Karman, E. E. Sechler, and L. H. Donnell. The strength of thin plates in compression. Transactions of ASME, 54: 53-7, 1932.
258. S. Levy. Bending of rectangular plates with large deflections. Technical Report 737, NACA, 1942.
259. S. Levy. Buckling of rectangular plates with built-in edges. Journal of Applied Mechanics, 9: 171-4, 1942.
260. H.-N. Chu and G. Herrmann. Influence of large amplitudes on free flexural vibrations of rectangular elastic plates. Journal of Applied Mechanics, 23: 532-40, 1956.
261. S. F. Bassily and S. M. Dickinson. Buckling and lateral vibration of rectangular plates subject to in-plane loads-a Ritz approach. Journal of Sound and Vibration, 24: 219-39, 1972.
262. S. M. Dickinson. The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using Rayleigh's method. Journal of Sound and Vibration, 61: 1-8, 1978.
263. C. F. Ng and R. G. White. Dynamic behavior of postbuckled isotropic plates under in-plane compression. Journal of Sound and Vibration, 120: 1-18, 1988.
264. G. H. Bryan. On the stability of a plane plate under thrusts in its own plane with applications to the buckling of the sides of a ship. Proceedings of the London Mathematical Society, 22: 54-67, 1891.
265. S. Ilanko. Vibration and post-buckling of in-plane loaded rectangular plates using a multiterm Galerkin's method. Journal of Applied Mechanics, 69: 589-92, 2002.
266. A. C. Ugural. Stresses in Plates and Shells. McGraw-Hill, 1999.
267. G. Herrmann and J. Shaw. Vibration of thin shells under initial stress. Journal of Engineering Mechanics, 91: 37-59, 1965.
268. J. F. Doyle. Nonlinear Analysis of Thin-Walled Structures. Springer, 2001.
269. K. K. Kapur and B. J. Hartz. Stability of plates using the finite element method. Journal of Engineering Mechanics, 92: 177-95, 1966.
270. R. G. Anderson, B. M. Irons, and O. C. Zienkiewicz. Vibration and stability of plates using finite elements. International Journal of Solids and Structures, 4: 1031-55, 1968.
271. B. A. Boley and J. H. Weiner. Theory of Thermal Stresses. Wiley, 1960.
272. D. J. Johns. Thermal Stress Analysis. Pergamon, 1965.
273. J. Marcinowski. Postbuckling behaviour of rectangular plates in axial compression. Archives of Civil Engineering, 45: 275-88, 1999.
274. K. D. Murphy. Theoretical and experimental studies in nonlinear dynamics and stability of elastic structures. Ph. D. dissertation, Duke University, 1994.
275. R. E. Kielb and L. S. Han. Vibration and buckling of rectangular plates under in-plane hydrostatic loading. Journal of Sound and Vibration, 70: 543-55, 1980.
276. R. E. Kielb. Thermal buckling of uniform rectangular plates. Technical Report, U. S. Air Force Wright-Patterson, ASD-TR-75-37, 1976.
277. T. R. Tauchert. Thermally induced flexure, buckling, and vibration of plates. Applied Mechanics Reviews, 44: 347-60, 1991.
278. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. The effect of thermal prestress on the free vibration characteristics of clamped rectangular plates: Theory and experiment. Journal of Vibration and Acoustics, 119: 243-9, 1997.
279. M. Stein. Loads and deformation of buckled rectangular plates. Technical Report R-40, NASA, 1959.
280. D. G. Schaeffer and M. Golubitsky. Boundary conditions and mode jumping in the buckling of rectangular plates. Communications in Mathematics and Physics, 69: 209-36, 1979.
281. R. Maaskant and J. Roorda. Mode jumping in biaxially compressed plates. International Journal of Solids and Structures, 29: 1209-19, 1991.
282. H. Chen and L. N. Virgin. Finite element analysis of postbuckling dynamics in plates: Part I: An asymptotic approach. International Journal of Solids and Structures, 43: 3983-4007, 2006.
283. H. Chen and L. N. Virgin. Finite element analysis of postbuckling dynamics in plates: Part II: A nonstationary analysis. International Journal of Solids and Structures, 43: 4008-27, 2006.
284. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Characterizing the dynamic response of a thermally loaded, acoustically excited plate. Journal of Sound and Vibration, 196: 635-58, 1996.
285. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Experimental snap-through boundaries for acoustically excited, thermally buckled plates. Experimental Mechanics, 36: 312-7, 1996.
286. L. N. Virgin. Parametric studies of the dynamic evolution through a fold. Journal of Sound and Vibration, 110: 99-109, 1986.
287. R. V. Southwell. On the analysis of experimental observations in problems of elastic stability. Proceedings of the Royal Society of London, 135A: 601-16, 1932.
288. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Free vibration of thermally loaded panels including initial imperfections and post-buckling effects. Technical Memorandum 109097, NASA, 1994.
289. M. Uemura and O. Byon. Secondary buckling of a flat plate under uniaxial compression-Part 1: Theoretical analysis of simply supported flat plate. International Journal of Non-Linear Mechanics, 12: 355-70, 1977.
290. E. Riks, C. C. Rankin, and F. A. Brogan. On the solution of mode jumping phenomena in thin-walled shell structures. Computer Methods in Applied Mechanics and Engineering, 36: 59-92, 1996.
291. H. Troger and A. Steindl. Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists. Springer-Verlag, 1991.
292. P. R. Everall and G. W. Hunt. Mode jumping in the buckling of struts and plates: A comparative study. International Journal of Non-Linear Mechanics, 35: 1067-79, 2000.
293. G. W. Hunt and P. R. Everall. Arnold tongues and mode-jumping in the supercritical post-buckling of an archetypal elastic structure. Proceedings of the Royal Society of London A, 445: 125-40, 1999.
294. T. Nakamura and K. Uetani. The secondary buckling and post-buckling behaviors of rectangular plates. International Journal of Mechanical Sciences, 21: 265-86, 1979.
295. E. J. Doedel. AUTO-Software for continuation and bifurcation problems in ordinary differential equations. California Institute of Technology, 1986.
296. E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. J. Wang. Auto97: Continuation and bifurcation software for ordinary differential equations. Technical Report, Department of Computer Science, Concordia University, Montreal, Canada, 1997 (available by FTP from ftp. cs. concordia. ca in directory pub/doedel/auto).
297. W. J. Supple. On the change in buckle pattern in elastic structures. International Journal of Mechanical Sciences, 10: 737-45, 1968.
298. J. M. T. Thompson and H. B. Stewart. Nonlinear Dynamics and Chaos, 2nd ed. Wiley, 2002.
299. H. Chen. Nonlinear analysis of post-buckling dynamics and higher order instabilities of flexible structures. Ph. D. dissertation, Duke University, 2004.
300. A. W. Leissa. Vibration of shells. Technical Report SP-288, NASA, 1973.
301. E. H. Dowell. Aeroelasticity of Plates and Shells. Noordhoff, 1975.
302. T. von Karman and H. S. Tsien. The buckling of thin cylindrical shells under axial compression. Journal of the Aeronautical Sciences, 8: 303-12, 1941.
303. L. H. Donnell. A new theory for the buckling of thin cylinders under axial compression and bending. Transactions of ASME, 56: 796-806, 1934.
304. R. D. Blevins. Formulas for Natural Frequencies and Mode Shapes. Van Nostrand Rheinhold, 1979.
305. K. Forsberg. A review of analytical methods used to determine the modal characteristics of cylindrical shells. NASA Report CR-613, Lockheed Aircraft Company, CA, September 1966.
306. S. B. Batdorf. A simplified method of elastic-stability analysis for thin cylindrical shells. Technical Report 874, NACA, 1947.
307. A. E. Armenakas. Influence of initial stress on the vibrations of simply supported circular cylindrical shells. AIAA Journal, 2: 1607-12, 1964.
308. H. S. Shen. Thermomechanical post-buckling analysis of imperfect laminated plates using a higher-order shear-deformation theory. Computers and Structures, 66: 395-409, 1998.
309. C.-S. Chen and C.-P. Fung. Non-linear vibration of initially stressed hybrid composite plates. Journal of Sound and Vibration, 274: 1013-29, 2004.
310. R. G. Parker and C. D. Mote. Tuning of the natural frequency spectrum of a circular plate by in-plane stress. Journal of Sound and Vibration, 145: 95-110, 1991.
311. J. H. Ginsberg. Advanced Engineering Dynamics. Cambridge University Press, 1995.
312. F. Bleich. Buckling Strength of Metal Structures. McGraw-Hill, 1952.
313. C. Massonnet. Les relations entre les modes normaux de vibration et la stabilité des systemes élastiques. Technical Report, Bulletin des cours et des laboratoires d'essais des constructions du genie civil et d'hydraulique fluviale, Brussels, Belgium, I (1, 2), 1-353, 1940.
314. H. Lurie. Lateral vibrations as related to structural stability. Journal of Applied Mechanics, 19: 195-204, 1952.
315. C. Sundararajan. Frequency analysis of axially loaded structures. AIAA Journal, 30: 1139-41, 1992.
316. R. V. Southwell. On the analysis of experimental observations in problems of elastic stability. Proceedings of the Royal Society of London, 135A: 601-16, 1932.
317. J. Ari-Gur, T. Weller, and J. Singer. Experimental and theoretical studies of columns under axial loading. International Journal of Solids and Structures, 18: 619-41, 1982.
318. M. A. Souza. The effects of initial imperfection and changing support conditions on the vibration of structural elements liable to buckling. Thin-Walled Structures, 5: 411-23, 1987.
319. R. G. White. Evaluation of the dynamic characteristics of structures by transient testing. Journal of Sound and Vibration, 15: 147-61, 1971.
320. A. Segall and M. Baruch. A nondestructive dynamic method for the determination of the critical load of elastic columns. Experimental Mechanics, 20: 285-8, 1980.
321. P. M. Mujumdar and S. Suryanarayan. Nondestructive techniques for prediction of buckling loads-a review. Journal of the Aeronautical Society of India, 41: 205-23, 1989.
322. M. A. Souza and L. M. B. Assaid. A new technique for the prediction of buckling loads from nondestructive vibration tests. Experimental Mechanics, 31: 93-7, 1991.
323. J. Singer, J. Arbocz, and T. Weller. Buckling Experiments, Vol. 1. Wiley, 1998.
324. J. Singer, J. Arbocz, and T. Weller. Buckling Experiments, Vol. 2. Wiley, 2002.
325. J. G. A. Croll and A. C. Walker. Elements of Structural Stability. Wiley, 1972.
326. C. R. Farrar, S. W. Doebling, and D. A. Nix. Vibration-based structural damage identification. Philosophical Transactions of the Royal Society, A359: 131-49, 2001.
327. A. Sommerfeld. Eine einfache Vorrichtung zur veranschaulichung des Knickungsvorganges. Zeitschrift des Verein deutscher Ingenieure, pp. 1320-3, 1905.
328. A. B. Pippard. Response and Stability. Cambridge University Press, 1985.
329. T. D. Burton. Introduction to Dynamic Systems Analysis. McGraw-Hill, 1994.
330. A. Segall and G. S. Springer. A dynamic method for measuring the critical loads of elastic flat panels. Experimental Mechanics, 26: 354-9, 1986.
331. T. Livingston, J. G. Béliveau, and D. R. Huston. Estimation of axial load in prismatic members using flexural vibrations. Journal of Sound and Vibration, 179: 899-908, 1995.
332. A. L. Sweet and J. Genin. Identification of a model for predicting elastic buckling. Journal of Sound and Vibration, 14: 317-24, 1971.
333. A. L. Sweet, J. Genin, and P. F. Mlakar. Determination of column-buckling criteria using vibratory data. Experimental Mechanics, 17: 385-91, 1977.
334. D. J. Inman. Engineering Vibration. Prentice Hall, 2000.
335. P.-Y. Shih and H. L. Schreyer. Lower bounds to fundamental frequencies and buckling loads of columns and plates. International Journal of Solids and Structures, 14: 1013-26, 1978.
336. K. Huseyin and J. Roorda. The loading-frequency relationship in multiple eigenvalue problems. Journal of Applied Mechanics, 38: 1007-11, 1971.
337. K. Huseyin. Multiple Parameter Stability Theory and Its Applications. Oxford University Press, 1986.
338. L. N. Virgin. Parametric studies of the dynamic evolution through a fold. Journal of Sound and Vibration, 110: 99-109, 1986.
339. L. N. Virgin and R. H. Plaut. Use of frequency data to predict secondary bifurcation. Journal of Sound and Vibration, 251: 919-26, 2002.
340. A. Chailleux, Y. Hans, and G. Verchery. Experimental study of the buckling of laminated composite columns and plates. International Journal of Mechanical Sciences, 17: 489-98, 1975.
341. R. H. Plaut and L. N. Virgin. Use of frequency data to predict buckling. Journal of Engineering Mechanics, 116: 2330-5, 1990.
342. R. H. Plaut and E. R. Johnson. The effect of initial thrust and elastic foundation on the vibration frequencies of a shallow arch. Journal of Sound and Vibration, 78: 565-71, 1981.
343. J. E. M. Jubb, I. G. Phillips, and H. Becker. Interrelation of structural stability, stiffness, residual stress and natural frequency. Journal of Sound and Vibration, 39: 121-34, 1975.
344. F. W. Williams, P. N. Bennett, and D. Kennedy. Curves for natural frequencies of axially compressed prismatic plate assemblies. Journal of Sound and Vibration, 194: 13-24, 1996.
345. P. N. Bennett and F. W. Williams. Insight into the sensitivity to axial compressive load of the natural frequencies of structures which include shear deformation. Journal of Sound and Vibration, 209: 707-22, 1998.
346. R. R. Archer. On the influence of uniform stress states on the natural frequencies of spherical shells. Journal of Applied Mechanics, pp. 502-5, September 1962.
347. J. F. Wilson. Dynamics of Offshore Structures. Wiley, 2002.
348. Y. Bai and Q. Bai. Subsea Pipelines and Risers. Elsevier, 2005.
349. M. S. El Naschie. Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw-Hill, 1990.
350. D. W. Jordan and P. Smith. Nonlinear Ordinary Differential Equations. Oxford University Press, 1999.
351. S. P. Timoshenko and J. M. Gere. Theory of Elastic Stability, 2nd ed. McGraw-Hill, 1961.
352. J. P. Cusumano. Low-Dimensional, Chaotic, Nonplanar Motions of the Elastica: Experiment and Theory. Ph. D. dissertation, Cornell University, 1990.
353. C. Gatti-Bono and N. C. Perkins. Dynamic analysis of loop formation in cables under compression. International Journal of Offshore and Polar Engineering, 12: 217-22, 2002.
354. D. Addessi, W. Lacarbonara, and A. Paolone. On the linear normal modes of planar pre-stressed curved beams. Journal of Sound and Vibration, 284: 1075-97, 2005.
355. L. N. Virgin and R. H. Plaut. Postbuckling and vibrations of linearly elastic and softening columns under self-weight. International Journal of Solids and Structures, 41: 4989-5001, 2004.
356. R. H. Plaut and L. N. Virgin. Three-dimensional postbuckling and vibration of vertical half-loop under self-weight. International Journal of Solids and Structures, 41: 4975-88, 2004.
357. C. J. Goh and C. M. Wang. Generalized shooting method for elastic stability analysis and optimization of structural members. Computers and Structures, 38: 73-81, 1990.
358. M. A. Crisfield. Nonlinear Finite Element Analysis of Solids and Structures, Vol. 2: Advanced Topics. Wiley, 1997.
359. A. G. Greenhill. Determination of the greatest height consistent with stability that a vertical pole or mast can be made, and of the greatest height to which a tree of given proportions can grow. Proceedings of the Cambridge Philosophical Society, 4: 65-73, 1881.
360. K. Huseyin. Multiple Parameter Stability Theory and Its Applications. Oxford University Press, 1986.
361. R. Schmidt and D. A. DaDeppo. Large deflection of heavy cantilever beams and columns. Quarterly Journal of Applied Mathematics, 28: 441-4, 1970.
362. C. Y. Wang. A critical review of the heavy elastica. International Journal of Mechanical Sciences, 28: 549-59, 1986.
363. S.-B. Hsu and S.-F. Hwang. Analysis of large deformation of a heavy cantilever. SIAM Journal on Mathematical Analysis, 19: 854-66, 1988.
364. S. Santillan, L. N. Virgin, and R. H. Plaut. Post-buckling and vibration of heavy beam on horizontal or inclined rigid foundation. Journal of Applied Mechanics, 73: 664-71, 2006.
365. S. Santillan, L. N. Virgin, and R. H. Plaut. Equilibria and vibration of a heavy pinched loop. Journal of Sound and Vibration, 288: 81-90, 2005.
366. J. G. A. Croll. Some comments on the mechanics of thermal buckling. The Structural Engineer, 83: 127-32, 2005.
367. N. C. Perkins. Planar vibration of an elastica arch: Theory and experiment. Journal of Vibration and Acoustics, 112: 374-9, 1990.
368. H. G. McComb. Large deflection of a cantilever beam under arbitrarily directed tip load. Technical Report, Technical Memorandum 86442, NASA Langley Research Center, 1985.
369. E. Riks. The application of Newton's method to the problem of elastic stability. Journal of Applied Mechanics, 39: 1060-6, 1972.
370. D. B. Holland, I. Stanciulescu, L. N. Virgin, and R. H. Plaut. Vibration and large deflection of cantilevered elastica compressed by angled cable. AIAA Journal, 44: 1468-76, 2006.
371. T. G. Beckwith, R. D. Marangoni, and J. H. Lienhard. Mechanical Measurements. Addison-Wesley, 1993.
372. I. Stanciulescu, L. N. Virgin, and T. A. Laursen. Finite element analysis of slender solar sail booms. Journal of Spacecraft and Rockets, 44: 528-37, 2007.
373. D. B. Holland, L. N. Virgin, and R. H. Plaut. Large deflections and vibration of a tapered cantilever pulled at its tip by a cable. Journal of Sound and Vibration, 2007, to appear.
374. J. H. Meier. On the dynamics of elastic buckling. Journal of the Aeronautical Sciences, 12: 433-40, 1945.
375. J. F. Davidson. Buckling of struts under dynamic loading. Journal of the Mechanics and Physics of Solids, 2: 54-66, 1953.
376. G. Herrmann. Dynamic Stability of Structures. Pergamon, 1967.
377. G. J. Simitses, A. N. Kounadis, and J. Giri. Dynamic buckling of simple frames under a step load. Journal of Engineering Mechanics, 105: 896-900, 1979.
378. A. T. Brewer and L. A. Godoy. On interaction between static and dynamic loads in instability of symmetric or asymmetric structural systems. Journal of Sound and Vibration, 147: 105-14, 1991.
379. I. Cochin and H. P. Plass. Analysis and Design of Dynamic Systems. Harper & Row, 1990.
380. B. Budiansky. Dynamic buckling of elastic structures: Criteria and estimates. In G. Herrmann, editor, Dynamic Stability of Structures. Pergamon, 1967.
381. G. J. Simitses. Effect of static preloading on the dynamic stability of structures. AIAA Journal, 21: 1174-80, 1983.
382. J. M. T. Thompson. Dynamic buckling under step loading. In G. Herrmann, editor, Dynamic Stability of Structures. Pergamon, 1967.
383. J. Roorda. Stability of structures with small imperfections. Journal of the Engineering Mechanics Division, ASCE, 91: 87, 1965.
384. J. W. Hutchinson and B. Budiansky. Dynamic buckling estimates. AIAA Journal, 4: 525-30, 1966.
385. G. J. Simitses. Instability of dynamically-loaded structures. Applied Mechanics Reviews, 40: 1403-8, 1987.
386. G. A. Zizicas. Dynamic buckling of thin elastic plates. Transactions of the ASME, 74: 1257-68, 1952.
387. P. S. Bulson. The Stability of Flat Plates. Chatto and Windus, 1970.
388. B. Budiansky and E. S. Roth. Axisymmetric dynamic buckling of clamped shallow spherical shells. Technical Report, NASA TND-1510, 1962.
389. M. W. Hilburger, A. M. Waas, and J. H. Starnes. Modeling the dynamic response and establishing post buckling snap-through equilibrium of discrete structures via a transient analysis. Journal of Applied Mechanics, 64: 590-5, 1997.
390. D. J. Inman. Engineering Vibration. Prentice-Hall, 2000.
391. L. N. Virgin. Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration. Cambridge University Press, 2000.
392. J. M. T. Thompson. Chaotic phenomena triggering escape from a potential well. Proceedings of the Royal Society of London, A421: 195-225, 1989.
393. L. N. Virgin, R. H. Plaut, and C.-C. Cheng. Prediction of escape from a potential well under harmonic excitation. International Journal of Non-Linear Mechanics, 27: 357-65, 1992.
394. J. A. Gottwald, L. N. Virgin, and E. H. Dowell. Routes to escape from an energy well. Journal of Sound and Vibration, 187: 133-44, 1995.
395. G. J. Simitses. Dynamic Stability of Suddenly Loaded Structures. Springer-Verlag, 1989.
396. D. L. C. Lo and E. F. Masur. Dynamic buckling of shallow arches. Journal of the Engineering Mechanics Division, ASCE, 102: 901-17, 1976.
397. C. S. Hsu. Stability of shallow arches against snap-through under timewise step loads. Journal of Applied Mechanics, 35: 31-9, 1968.
398. R. H. Plaut and E. R. Johnson. The effect of initial thrust and elastic foundation on the vibration frequencies of a shallow arch. Journal of Sound and Vibration, 78: 565-71, 1981.
399. N. J. Hoff and V. G. Bruce. Dynamic analysis of the buckling of laterally loaded flat arches. Journal of Mathematical Physics, 32: 276-88, 1954.
400. A. M. Liapunov. Stability of Motion (Collected Papers). Academic, 1966.
401. R. E. Fulton and F. W. Barton. Dynamic buckling of shallow arches. Journal of Engineering Mechanics, 97: 865-77, 1971.
402. K.-Y. Huang and R. H. Plaut. Snap-through of a shallow arch under pulsating load. In F. H. Schroeder, editor, Stability in the Mechanics of Continua. Springer, 1982, pp. 215-33.
403. M. T. Donaldson and R. H. Plaut. Dynamic stability boundaries for a sinusoidal shallow arch under pulse loads. AIAA Journal, 21: 469-71, 1983.
404. E. R. Johnson and I. K. McIvor. The effect of spatial distribution on dynamic snapthrough. Journal of Applied Mechanics, 45: 612-18, 1978.
405. R. H. Plaut and J.-C. Hsieh. Oscillations and instability of a shallow arch under twofrequency excitation. Journal of Sound and Vibration, 102: 189-201, 1985.
406. J. S. Humphreys and S. R. Bodner. Dynamic buckling of shallow shells under impulsive loading. Journal of Engineering Mechanics, 88: 17-36, 1962.
407. W. B. Krätzig. Nonlinear responses. In A. N. Kounadis and W. B. Krätzig, editors, Nonlinear Stability of Structures (Theory and Computational Techniques). Springer-Verlag, 1995.
408. W. B. Krätzig and P. Nawrotzki. Computational concepts for kinetic instability problems. In A. N. Kounadis and W. B. Krätzig, editors, Nonlinear Stability of Structures (Theory and Computational Techniques). Springer-Verlag, 1995.
409. W. B. Krätzig. Eine einheitliche statische und dynamische Stabilitatstheorie fur Pfadverfolgungsalgorithmen in der numerischen Festkorpermechanik. Zeitschrift für Angewandte Mathematik und Mechanik, 69: 203-13, 1989.
410. D. Dinkler and J. Pontow. A model to evaluate dynamic stability of imperfection sensitive shells. Computational Mechanics, 37: 523-9, 2006.
411. C. Koning and J. Taub. Impact buckling of thin bars in the elastic range hinged at both ends. Luftfahrforschung, 10: 55-64, 1933.
412. G. Gerard and H. Becker. Column behavior under conditions of impact. Journal of the Aeronautical Sciences, 19: 58-60, 1952.
413. E. Sevin. On the elastic bending of columns due to dynamic axial forces including effects of axial inertia. Journal of Applied Mechanics, 27: 125-31, 1960.
414. R. Grybos. Impact stability of a bar. International Journal of Engineering Science, 13: 463-77, 1975.
415. N. J. Huffington. Response of elastic columns to axial pulse loading. AIAA Journal, 1: 2099-2104, 1963.
416. I. K. McIvor and J. E. Bernard. The dynamic response of columns under short duration axial loads. Journal of Applied Mechanics, 40: 688-92, 1973.
417. J. M. Housner and N. F. Knight. The dynamic collapse of a column impacting a rigid surface. AIAA Journal, 21: 1187-95, 1983.
418. W. Abramowicz and N. Jones. Dynamic progressive buckling of circular and square tubes. International Journal of Impact Engineering, 4: 247-70, 1986.
419. H. E. Lindberg and A. L. Florence. Dynamic Pulse Buckling: Theory and Experiment. Nijhoff, 1987.
420. S. M. Holzer and R. A. Eubanks. Stability of columns subjected to impulsive loading. Journal of Engineering Mechanics, 95: 897-920, 1969.
421. T. Hayashi and Y. Sano. Dynamic buckling of elastic bars (the case of low velocity impact). Bulletin of the Japanese Society of Mechanical Engineering, 15: 1167-75, 1972.
422. T. Hayashi and Y. Sano. Dynamic buckling of elastic bars (the case of high velocity impact). Bulletin of the Japanese Society of Mechanical Engineering, 15: 1176-84, 1972.
423. J. R. Gladden, N. Z. Handzy, A. Belmonte, and E. Villermaux. Dynamic buckling and fragmentation in brittle rods. Physical Review Letters, 94(035503), 2005.
424. I. Elishakoff. Axial impact buckling of a column with random initial imperfections. Journal of Applied Mechanics, 45: 361-5, 1978.
425. H. E. Lindberg and R. E. Herbert. Dynamic buckling of a thin cylindrical shell under axial impact. Journal of Applied Mechanics, 33: 105-12, 1966.
426. N. Jones and C. S. Ahn. Dynamic elastic and plastic buckling of complete spherical shells. International Journal of Solids and Structures, 10: 1357-74, 1974.
427. R. Kao. Nonlinear dynamic buckling of spherical caps with initial imperfections. Computers and Structures, 12: 49-63, 1980.
428. N. J. Hoff. The dynamics of the buckling of elastic columns. Journal of AppliedMechanics, 17: 68-74, 1953.
429. J. Singer, J. Arbocz, and T. Weller. Buckling Experiments, Vol. 2. Wiley, 2002.
430. A. H. Nayfeh and D. T. Mook. Nonlinear Oscillations. Wiley, 1979.
431. S. K. Sinha. Dynamic stability of a timoshenko beam subjected to an oscillating axial force. Journal of Sound and Vibration, 131: 509-14, 1989.
432. R. M. Evan-Iwanowski. On the parametric response of structures. Applied Mechanics Reviews, 18: 699-702, 1965.
433. D. Krajcinovic and G. Herrmann. Parametric resonance of straight bars subjected to repeated impulsive compression. AIAA Journal, 6: 2025-7, 1968.
434. A. D. S. Barr and G. T. S. Done. Parametric oscillations in aircraft structures. The Aeronautical Journal, 75: 654-8, 1971.
435. C. E. Hammond. An application of Floquet theory to prediction of mechanical instability. Journal of the American Helicopter Society, 4: 14-23, 1974.
436. R. A. Ibrahim and A. D. S. Barr. Parametric resonance, part I: Mechanics of linear problems. Shock and Vibration Digest, 10(1): 15-29, 1978.
437. R. A. Ibrahim and A. D. S. Barr. Parametric resonance, part II: Mechanics of nonlinear problems. Shock and Vibration Digest, 10(2): 9-24, 1978.
438. G. J. Simitses. Dynamic Stability of Suddenly Loaded Structures. Springer-Verlag, 1989.
439. J. P. Cusumano. Low-Dimensional, Chaotic, Nonplanar Motions of the Elastica: Experiment and Theory. Ph. D. dissertation, Cornell University, 1990.
440. C. Hayashi. Nonlinear Oscillations in Physical Systems. Princeton University Press, 1964.
441. V. V. Bolotin. The Dynamic Stability of Elastic Systems. Holden-Day, 1964.
442. M. A. Souza. Vibration of thin-walled structures with asymmetric post-buckling characteristics. Thin-Walled Structures, 14: 45-57, 1992.
443. D. W. Jordan and P. Smith. Nonlinear Ordinary Differential Equations. Oxford University Press, 1999.
444. J. Guckenheimer and P. J. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.
445. N. W. McLachlan. Theory and Applications of Mathieu Functions. Dover, 1964.
446. Z. P. Bazant and L. Cedolin. Stability of Structures. Oxford University Press, 1991.
447. J. F. Doyle. Nonlinear Analysis of Thin-Walled Structures. Springer, 2001.
448. E. Ott. Chaos in Dynamical Systems. Cambridge University Press, 1993.
449. P. R. Everall and G. W. Hunt. Arnold tongue predictions of secondary buckling in thin elastic plates. Journal of the Mechanics and Physics of Solids, 47: 2187-2206, 1999.
450. P. R. Everall and G. W. Hunt. Quasi-periodic buckling of an elastic structure under the influence of changing boundary conditions. Proceedings of the Royal Society of London A, 455: 3041-51, 1999.
451. K. K. V. Devarakonda and C. W. Bert. Flexural vibration of rectangular plates subjected to sinusoidal distributed compressive loading on two opposite sides. Journal of Sound and Vibration, 283: 749-63, 2005.
452. Y. Basar, C. Eller, and W. B. Krätzig. Finite element procedures for parametric phenomena of arbitrary elastic shell structures. Computational Mechanics, 2: 89-98, 1987.
453. W. B. Krätzig and P. Nawrotzki. Computational concepts for kinetic instability problems. In A. N. Kounadis and W. B. Krätzig, editors, Nonlinear Stability of Structures (Theory and Computational Techniques). Springer-Verlag, 1995.
454. A. A. Popov, J. M. T. Thompson, and J. G. A. Croll. Bifurcation analyses in the parametrically excited vibrations of cylindrical panels. Nonlinear Dynamics, 17: 205-25, 1998.
455. A. A. Popov. Parametric resonance in cylindrical shells: A case study in the nonlinear vibration of structural shells. Engineering Structures, 25: 789-99, 2003.
456. A. A. Popov, J. M. T. Thompson, and F. A. McRobie. Low dimensional models of shell vibrations: Parametrically excited vibrations of cylindrical shells. Journal of Sound and Vibration, 209: 163-86, 1998.
457. F. A. McRobie, A. A. Popov, and J. M. T. Thompson. Auto-parametric resonance in cylindrical shells using geometric averaging. Journal of Sound and Vibration, 227: 65-84, 1999.
458. C. S. Hsu. Impulsive parametric excitation: Theory. Journal of Applied Mechanics, 39: 551-8, 1972.
459. N. HaQuang, D. T. Mook, and R. H. Plaut. A non-linear analysis of the interactions between parametric and external excitations. Journal of Sound and Vibration, 118: 425-39, 1987.
460. T. Iwatsubo, Y. Sugiyama, and S. Ogino. Simple and combination resonances of columns under periodic axial loads. Journal of Sound and Vibration, 33: 211-21, 1974.
461. R. H. Plaut, N. HaQuang, and D. T. Mook. Simultaneous resonances in non-linear structural vibrations under two-frequency excitation. Journal of Sound and Vibration, 106: 361-76, 1986.
462. A. P. Seyranian and A. A. Mailybaev. Multiparameter Stability Theory with Mechanical Applications. World Scientific, 2003.
463. C.-H. Xei. Dynamic Stability of Structures. Cambridge University Press, 2006.
464. L. N. Virgin and R. H. Plaut. Effect of axial load on forced vibrations of beams. Journal of Sound and Vibration, 168: 395-405, 1993.
465. D. J. Ewins. Modal Testing: Theory and Practice. Research Studies Press, 1984.
466. W. T. Thomson. Theory of Vibration with Applications. Prentice Hall, 1981.
467. D. J. Inman. Engineering Vibration. Prentice Hall, 2000.
468. D. W. Jordan and P. Smith. Nonlinear Ordinary Differential Equations. Oxford University Press, 1999.
469. J. Guckenheimer and P. J. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.
470. K. Ogata. System Dynamics. Prentice Hall, 1998.
471. G. C. Goodwin and R. L. Payne. Dynamics System Identification: Experiment Design and Data Analysis. Academic, 1977.
472. A. Picard, D. Beaulieu, and B. Perusse. Rotational restraint of a simple column base connection. Canadian Journal of Civil Engineering, 14: 49-57, 1987.
473. R. H. Plaut. Column buckling when support stiffens under compression. Journal of Applied Mechanics, 56: 484, 1989.
474. F. C. Nelson. Vibration isolation: A review, I. Sinusoidal and random excitations. Shock and Vibration, 1: 485-93, 1994.
475. R. H. Racca. Characteristics of vibration isolators and isolation systems. In Shock and Vibration Handbook, 4th ed. McGraw-Hill, 1996, Chapter 32.
476. J. Winterflood, T. Barber, and D. G. Blair. High performance vibration isolation using spring in Euler column buckling mode. Physics Letters A, 19: 1639-45, 2002.
477. E. I. Rivin. Passive Vibration Isolation. ASME, 2003.
478. L. N. Virgin and R. B. Davis. Vibration isolation using buckled struts. Journal of Sound and Vibration, 260: 965-73, 2003.
479. R. H. Plaut, J. E. Sidbury, and L. N. Virgin. Analysis of buckled and pre-bent fixed-end columns used as vibration isolators. Journal of Sound and Vibration, 283: 1216-28, 2005.
480. J. Jiang and E. Mockensturm. Amotion amplifier using an axially driven buckling beam: I. Design and experiments. Nonlinear Dynamics, 43: 391-409, 2006.
481. J. Jiang and E. Mockensturm. Amotion amplifier using an axially driven buckling beam: II. Modeling and analysis. Nonlinear Dynamics, 45: 1-14, 2006.
482. E. S. Leland and P. K. Wright. Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial load. Smart Materials and Structures, 15: 1413-20, 2006.
483. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Experimental snap-through boundaries for acoustically excited, thermally buckled plates. Experimental Mechanics, 36: 312-17, 1996.
484. L. N. Virgin. Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration. Cambridge University Press, 2000.
485. D. E. Newland. An Introduction to Random Vibrations and Spectral Analysis. Longman, 1984.
486. J. S. Bendat and A. G. Piersol. Random Data: Analysis and Measurement Procedures. Wiley, 1986.
487. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Characterizing the dynamic response of a thermally loaded, acoustically excited plate. Journal of Sound and Vibration, 196: 635-58, 1996.
488. P. Hagedorn. Nonlinear Oscillations. Clarendon, 1981.
489. N. Krylov and N. Bogoliubov. Introduction to Non-Linear Mechanics. Princeton University Press, 1949.
490. T. Wah. Large amplitude flexural vibration of rectangular plates. International Journal of Mechanical Sciences, 5: 425-38, 1963.
491. D. W. Jordan and P. Smith. Nonlinear Ordinary Differential Equations. Oxford University Press, 1999.
492. C. Hayashi. Nonlinear Oscillations in Physical Systems. Princeton University Press, 1964.
493. A. H. Nayfeh and D. T. Mook. Nonlinear Oscillations. Wiley, 1979.
494. J. Kevorkian and J. D. Cole. Perturbation Methods in Applied Mathematics. Springer-Verlag, 1981.
495. L. N. Virgin. Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration. Cambridge University Press, 2000.
496. J. A. Gottwald, L. N. Virgin, and E. H. Dowell. Experimental mimicry of Duffing's equation. Journal of Sound and Vibration, 158: 447-67, 1992.
497. G. H. Argyris and H.-P. Mlejnek. Dynamics of Structures. North-Holland, 1991.
498. N. B. Tufillaro, T. Abbott, and J. Reilly. An Experimental Approach to Nonlinear Dynamics and Chaos. Addison-Wesley, 1992.
499. K. D. Murphy. Theoretical and experimental studies in nonlinear dynamics and stability of elastic structures. Ph. D. dissertation, Duke University, 1994.
500. H. Chen. Nonlinear analysis of post-buckling dynamics and higher order instabilities of flexible structures. Ph. D. dissertation, Duke University, 2004.
501. J. W. Miles. Resonant, nonplanar motion of a stretched string. Journal of the Acoustical Society of America, 75: 1505-10, 1984.
502. G. Duffing. Erzwungene Schwingungen bei veranderlicher Eigenfrequenz. F. Vieweg u. Sohn, 1918.
503. H. M. Irvine. Cable Structures. MIT Press, 1981.
504. O. M. O'Reilly and P. J. Holmes. Non-linear, non-planar and non-periodic vibrations of a string. Journal of Sound and Vibration, 153: 413-35, 1992.
505. N. Yamaki and A. Mori. Non-linear vibrations of a clamped beam with initial deflection and initial axial displacement, part I: Theory. Journal of Sound and Vibration, 71: 333-46, 1980.
506. N. Yamaki, K. Otomo, and A. Mori. Non-linear vibrations of a clamped beam with initial deflection and initial axial displacement, part II: Experiment. Journal of Sound and Vibration, 71: 347-60, 1980.
507. J. G. Eisley. Large amplitude vibration of buckled beams and rectangular plates. AIAA Journal, 2: 2207-9, 1964.
508. G.-B. Min and J. G. Eisley. Nonlinear vibration of buckled beams. ASME Journal of Engineering for Industry, 94: 637-46, 1972.
509. A. H. Nayfeh, W. Kreider, and T. J. Anderson. Investigation of natural frequencies and mode shapes of buckled beams. AIAA Journal, 33: 1121-6, 1995.
510. W. Y. Tseng and J. Dugundji. Nonlinear vibrations of a buckled beam under harmonic excitation. Journal of Applied Mechanics, 38: 467-76, 1971.
511. W. T. Thomson. Theory of Vibration with Applications. Prentice Hall, 1981.
512. D. J. Inman. Engineering Vibration. Prentice Hall, 2000.
513. G. V. Rao and K. K. Raju. Large amplitude free vibration of beams-an energy approach, Zeitschrift für Angewandte Mathematik und Mechanik 83: 493-8, 2003.
514. A. V. Srinivasan. Large amplitude free oscillations of beams and plates. AIAA Journal, 3: 1951-3, 1965.
515. C. Mei. Nonlinear vibration of beams by matrix displacement method. AIAA Journal, 10: 355-7, 1972.
516. J. M. T. Thompson and G. W. Hunt. Elastic Instability Phenomena. Wiley, 1984.
517. H. Wagner. Large-amplitude free vibrations of a beam. Journal of Applied Mechanics, 82: 887-90, 1965.
518. A. W. Leissa. Vibration of plates. Technical Report SP-160, NASA, 1969.
519. S. P. Timoshenko and S. Woinowsky-Krieger. Theory of Plates and Shells, 2nd ed. McGraw-Hill, 1968.
520. H.-N. Chu and G. Herrmann. Influence of large amplitudes on free flexural vibrations of rectangular elastic plates. Journal of Applied Mechanics, 23: 532-40, 1956.
521. D. A. Evensen and R. E. Fulton. Some studies on the nonlinear dynamic response of shell-type structures. Technical Report, NASA TMX 56843, 1965.
522. J. M. Johnson and A. K. Bajaj. Amplitude modulated and chaotic dynamics in resonant motion of strings. Journal of Sound and Vibration, 128: 87-107, 1989.
523. L. Nicu and C. Bergaud. Experimental and theoretical investigations on nonlinear resonances of composite buckled microbridges. Journal of Applied Physics, 86: 5835-40, 1999.
524. B. L. Clarkson. Review of sonic fatigue technology. Technical Report, NASA Contract Report 4587, 1994.
525. K. D. Murphy, L. N. Virgin, and S. A. Rizzi. Experimental snap-through boundaries for acoustically excited, thermally buckled plates. Experimental Mechanics, 36: 312-17, 1996.
526. E. H. Dowell. Aeroelasticity of Plates and Shells. Noordhoff, 1975.
527. P. J. Holmes. Bifurcations to divergence and flutter in flow-induced oscillations. Journal of Sound and Vibration, 53: 471-503, 1977.
528. B. van der Pol. The nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers, 22: 1051-86, 1934.
529. R. L. Bisplinghoff, H. Ashley, and R. L. Halfman. Aeroelasticity. Addision-Wesley, 1955.
530. J. M. T. Thompson. Instabilities and Catastrophes in Science and Engineering. Wiley, 1982.
531. C. W. Gear. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall, 1971.
532. C. S. Ventress and E. H. Dowell. Comparison of theory and experiment for nonlinear flutter of loaded plates. AIAA Journal, 8: 2022-30, 1970.
533. P. J. Holmes. Nonlinear dynamics, chaos, and mechanics. Applied Mechanics Reviews, 43: 23-39, 1990.
534. J. M. T. Thompson and H. B. Stewart. Nonlinear Dynamics and Chaos, 2nd ed. Wiley, 2002.
535. D. E. Newland. An Introduction to Random Vibrations and Spectral Analysis. Longman, 1984.
536. V. Brunsden, J. Cortell, and P. J. Holmes. Power spectra of chaotic vibrations of a buckled beam. Journal of Sound and Vibration, 130: 1-25, 1989.
537. P. Grassberger and I. Procaccia. Measuring the strangeness of strange attractors. Physica D, 9: 189-208, 1983.
538. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano. Determining Lyapunov exponents from a time series. Physica D, 16: 285-317, 1985.
539. C. Grebogi, E. Ott, and J. A. Yorke. Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics. Science, 238: 632-8, 1987.
540. C. S. Hsu. Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear for Nonlinear Systems. Springer-Verlag, 1987.
541. E. Eschenazi, H. G. Solari, and R. Gilmore. Basins of attraction in driven dynamical systems. Physical Review A, 39: 2609-27, 1989.
542. H. E. Nusse and J. A. Yorke. Basins of attraction. Science, 271: 1376-80, 1996.
543. N. Sri Namachchivaya and M. M. Doyle. Chaotic motion of a shallow arch. In Proceedings of the 29th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA, New York, 1988, pp. 198-209.
544. J. J. Thomsen. Chaotic vibrations of non-shallow arches. Journal of Sound and Vibration, 153: 239-58, 1992.
545. M. J. Feigenbaum. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics, 19: 25-32, 1978.
546. S. H. Strogatz. Nonlinear Dynamics and Chaos. Addison-Wesley, 1994.
547. V. K. Melnikov. On the stability of the center for time periodic solutions. Transactions of the Moscow Mathematics Society, 12: 1-57, 1963.
548. J. Guckenheimer and P. J. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1983.
549. S. Wiggins. An Introduction to Applied Dynamical Systems Theory and Chaos. Springer-Verlag, 1990.
550. F. C. Moon and P. J. Holmes. A magneto elastic strange attractor. Journal of Sound and Vibration, 65: 275-96, 1979.
551. P. J. Holmes and F. C. Moon. Strange attractors and chaos in nonlinear mechanics. Journal of Applied Mechanics, 50: 1021-32, 1983.
552. F. C. Moon. Chaotic and Fractal Dynamics, An Introduction for Applied Scientists and Engineers. Wiley, 1992.