Fundamentals of Structural Stability

Fundamentals of Structural Stability

Volumn , Issue , 2006, Pages

  Simitses, George J ^a   Hodges, Dewey H ^b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85013799027     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-7506-7875-9.X5000-2     Document Type: Book

References (261)

1. Biezeno C.B., Grammel R. Engineering Dynamics 1956, Part IV, Blackie and Son Ltd., London, Vol. II.
2. Bleich F. Buckling Strength of Metal Structures 1952, McGraw-Hill Book Co., New York.
3. Bolotin V.V. Nonconservative Problems of the Theory of Elastic Stability 1963, (translated from the Russian), The Macmillan Co., New York. G. Herrmann (Ed.).
4. Bolotin V.V. The Dynamic Stability of Elastic Systems 1964, Holden-Day, Inc., San Francisco.
5. Bryan G.H. On the stability of elastic systems. Proc. Cambridge Phil. Soc. 1888, Vol. 6:199.
6. Bryan G.H. Buckling of plates. Proc. the London Math. Soc. 1891, Vol. 22:54.
7. Chetayev N.G. Sur la réciproque du théorème de Lagrange. Comptes Rendues 1930.
8. Chetayev N.G. Stability of Motion 1961, Translated from the second Russian, Pergamon Press, London. M. Nadler (Ed.).
9. Flügge W. Handbook of Engineering Mechanics 1962, chaps. 44 and 45, McGraw-Hill Book Company, New York.
10. Herrmann G. Stability of the equilibrium of elastic systems subjected to nonconservative forces. Applied Mechanics Review 1967, 20.
11. Hoff N.J. Buckling and stability. J. Royal Aero. Soc. 1954, Vol. 58(January).
12. Hoff N.J. The Analysis of Structures 1956, John Wiley & Sons, Inc., New York.
13. Koiter W.T. The Stability of Elastic Equilibrium. Thesis, Delft. 1945, (English translation NASA TT-F-10833, 1967).
14. Koiter W.T. Elastic stability and post-buckling behavior. Nonlinear Problems 1963, 257-275. University of Wisconsin Press, Madison. R.E. Langer (Ed.).
15. Krasovskii N.N. Stability of Motion 1963, Stanford University Press, Stanford, California. J.L. Brenner (Ed.).
16. Lagrange J.L. Mecanique Analytique 1788, Paris.
17. Lanczos C. The Variational Principles of Mechanics 1960, University of Toronto Press, Toronto.
18. Langhaar H.L. Energy Methods in Applied Mechanics 1962, John Wiley & Sons, Inc., New York.
19. LaSalle J.P., Lefschetz S. Stability of Liapunov's Direct Method with Applications 1961, Academic Press, New York.
20. Leipholz H. Stability Theory 1970, Academic Press, New York.
21. Liapunov A. Problèmé générale de la Stabilité du Mouvement," Traduit du Russe par E. Davaux. Annales de la Faculté des Sciences de Toulouse. Zéme série 1952, 9. 1907, Princeton University Press, Princeton.
22. Pearson C.E. General theory of elastic stability. Quarterly of Applied Mathematics 1956, Vol. 14:133.
23. Poincaré H. Sur le Equilibre d'une Masse Fluide Animée d'un Mouvement de Rotation. Acta Mathematica 1885, Vol. 7:259-380. Stockholm.
24. Thompson J.M.T. Basic principles in the general theory of elastic stability. J. of the Mechanics and Physics of Solids 1963, Vol. 11:13.
25. Timoshenko S.P. History of Strength of Materials 1953, McGraw-Hill Book Co., New York.
26. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1961, McGraw-Hill Book Co., New York.
27. Trefftz E. Zur Theorie der Stabilität des Elastischen Gleichgewichts. Zeitschr.f angew. Math. u. Mech 1933, 13:160.
28. Whittaker E.T. Analytical Dynamics 1944, Dover Publications, New York.
29. Ziegler H. Principles of Structural Stability 1968, Blaisdell Publishing Co., Waltham, Massachusetts.
30. Hayashi C. Nonlinear Oscillations in Physical Systems 1964, McGraw-Hill Book Co., New York.
31. Koiter W.T. The Stability of Elastic Equilibrium. Thesis, Delft 1945, (English translation NASA TT-F-10833, 1967).
32. Krasovskii N.N. Stability of Motion 1963, Translated from the Russian, Stanford University Press, Stanford, California. J.L. Brenner (Ed.).
33. LaSalle J.P., Lefschetz S. Stability of Liapunov's Direct Method With Applications 1961, Academic Press, New York.
34. Malkin I.G. Theory of Stability of Motion 1958, A.E.C. Translation 3352, Dept. of Commerce, U.S.A.
35. Pope G.G. On the bifurcational buckling of elastic beams, plates and shallow shells. The Aeronautical Quarterly 1968, 20(Feb.).
36. Sewell M.J. On the connexion between stability and the shape of the equilibrium surface. Journal of the Mechanics and Physics of Solids 1966, Vol. 14:203.
37. Stoker J.J. Nonlinear Vibrations 1950, Interscience Publishers, Inc., New York.
38. Thompson J.M.T. Basic principles in the general theory of elastic stability. Journal of the Mechanics and Physics of Solids 1963, Vol. 11:13.
39. Thompson J.M.T. Eigenvalue branching configurations and the Rayleigh-Ritz procedure. Quarterly of Appl. Math 1964, Vol. 22:244.
40. Whittaker E.T. Analytical Dynamics 1944, Dover Publications, New York.
41. Biezeno C.B., Grammel R. Engineering Dynamics 1956, Vol. II:428. Part IV, Blackie and Son Ltd., London.
42. Carslaw H.S., Jaeger J.C. Operational Methods in Applied Mathematics 1947, Chap. 11, Dover Publications, Inc., New York.
43. Churchill R.V. Operational Mathematics 1958, 252, McGraw-Hill Book Co., New York.
44. Courant R., Hilbert D. Methods of Mathematical Physics 1953, Vol. 1:295. Interscience Publishers, Inc., New York.
45. Hodges D.H. Finite rotation and nonlinear beam kinematics. Vertica 1987, 1:297-307.
46. Hodges D.H. Nonlinear Beam Theory for Engineers 2006, Chapter 6, American Institute of Aeronautics and Astronautics.
47. Hoff N.J. The Analysis of Structures 1956, John Wiley & Sons, Inc., New York.
48. Love A.E.H. Mathematical Theory of Elasticity 1944, New York, Dover Publications, New York. 4th edition.
49. Reissner E., Tsai W.T. Pure bending, stretching, and twisting of anisotropic cylindrical shells. Journal of Applied Mechanics 1972, 39:148-154.
50. Shames I.H. Mechanics of Deformable Solids 1964, Chap. 7, Prentice-Hall, Inc., Englewood Cliffs, N. J.
51. Southwell R.V. An Introduction to the Theory of Elasticity 1936, 425, Oxford at the Clarendon Press.
52. Thomson Wm.T. Vibration Theory and Applications 1965, 276, Prentice-Hall, Inc., Englewood Cliffs, N. J.
53. Timoshenko S.P. History of Strength of Materials 1953, 30-36, McGraw-Hill Book Co., New York.
54. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1961, 135, McGraw-Hill Book Co., New York.
55. Vlasov V.Z. Thin-Walled Elastic Beams 1961, National Science Foundation and Department of Commerce.
56. Almroth B.O., Meiler E., Brogan F.A. Computer Solutions for Static and Dynamic Buckling of Shells. Buckling of Structures, International Union of Theoretical and Applied Mathematics Symposium 1976, Springer-Verlag, Berlin, Germany.
57. Baker J.F., Home M.R., Roderick J.W. The behaviour of continuous stanchions. Proceedings of the Royal Society 1949, Vol. A-198:493. London, England.
58. Ball L.R. Computational Solution of Nonlinear Operator Equations 1969, John Wiley and Sons, Inc., New York.
59. Bellman R. Perturbation Techniques in Mathematics. Physics and Engineering 1969, Holt. Rinehart, and Winston, New York.
60. Bleich F. Die Knickfestigkeit elasticher Stabrerbindungen. Der Eisenbau 1919, Vol. 10:27.
61. Bleich F. Buckling Strength of Metal Structures 1952, McGraw-Hill Book Co., New York. H.H. Bleich (Ed.).
62. Britvec S.J. The Post-buckling Behavior of Frames 1960, Thesis presented to, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Cambridge University, at Cambridge, England.
63. Britvec S.J. The Stability of Elastic Systems 1973, Pergamon Press, Inc., New York.
64. Britvec S.J., Chilver H.A. Elastic buckling of rigidly-joined braced frames. Journal of the Engineering Mechanics Division, ASCE 1963, Vol. 89(No. EM6):217-255. Proc. Paper 3736.
65. Brush D.O., Almroth B.O. Buckling of Bars, Plates, and Shells 1975, McGraw-Hill Book Co., New York.
66. Chilver A.H. Buckling of a simple portal frame. Journal of the Mechanics and Physics of Solids 1956, Vol. 5:18.
67. Chwalla E. Die Stabilität lotrecht belasteter Rechteckrahmen. Der Bauingenieur 1938, Vol. 19:69.
68. Daniel J.W. The Approximate Minimization of Functionals 1971, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
69. Godley H.R.M., Chilver H.A. The elastic post-buckling behaviour of unbraced frames. International Journal of Mechanical Science 1967, Vol. 9:323.
70. Home M.R. Stability of elastic-plastic structures. Progress in Solid Mechanics 1961, North-Holland Publishing Co., Amsterdam, the Netherlands.
71. Horne M.R., Merchant W. The Stability of Frames 1965, Pergamon Press, London, England.
72. Huddleston J.V. Nonlinear buckling and snap-over of a two-bar frame. International Journal of Solids and Structures 1967, Vol. 3:1023-1030.
73. Koiter W.T. Post buckling analysis of a simple two-bar frame. Recent Progress in Applied Mechanics 1966, Almginst and Wiksell, Stockholm, Sweden.
74. Koiter W.T. On the Stability of Elastic Equilibrium. Doctor of Philosophy 1967, in partial fulfillment of the requirements for the degree of, English translation NASA TT-F-10833.
75. Kounadis A. The Dynamic Procedure for the Study of Stability of Rectangular Frames Subjected to Static or Dynamic Loads 1976, National Technical University Report, Athens, Greece.
76. Kounadis A.N., Giri J., Simitses G.J. Nonlinear stability analysis of an eccentrically loaded two-bar frame. Journal of Applied Mechanics 1977, Vol. 44(No. 4):701-706. Series E.
77. Livesley R.K. Application of electronic digital computers to some problems of structural analysis. Structural Engineer 1956, 161-167. Vol. 34, Institution of Structural Engineers, London, England, No. 6.
78. McMinn S.J. Matrices for Structural Analysis 1962, John Wiley and Sons, Inc., New York.
79. Merchant W. The failure load of rigid-jointed frameworks as influenced by stability. Structural Engineer 1954, Vol. 32:185-190. Institution of Structural Engineers, London, England, No. 7.
80. Merchant W. Critical loads of tall building frames. Structural Engineers 1955, Vol. 33:84-89. Institution of Structural Engineers, London, England,, No. 3.
81. Mohamed S.E., Simitses G.J. Buckling of flexibily-connected gabled frames. International Journal of Non-Linear Mechanics 1989, Vol. 24(No. 5):353-364.
82. Mohamed S.E., Simitses G.J. Stability and strength of rigid and semirigid plane frame-works. ASCE J. of Aerospace Engineering 1993, Vol. 6(No. 2):186-198.
83. Müller-Breslau H. Die graphische Statik der Bau-Konstructionen 1908, Vol. II:2. A. Kröner, Berlin, Germany.
84. Neider J.A., Mead R. A simplex method of function minimization. Computer Journal 1964, Vol. 7:308-313.
85. Ortega M.J. Numerical Analysis 1972, Academic Press, New York.
86. Roorda J.Feb. Stability of structures with small imperfections. Journal of the Engineering Mechanics Division, ASCE 1965, Vol. 91:87-106. No. EMI, Proc. Paper 4230.
87. Roorda J., Chilver H.A. Frame Buckling: An Illustration of the Perturbation Technique. Report No. 2 1969, Solid Mechanics Division, University of Waterloo, Canada.
88. Sewell M.J. The static perturbation technique in buckling problems. Journal of the Mechanics and Physics of Solids 1965, Vol. 13:247.
89. Simitses G.J., Giri J. Asymmetrically loaded portal frames. Computers and Structures 1984, Vol. 19(No. 4):555-558.
90. Simitses G.J., Mohamed S.E. Instability and collapse of flexibly-connected gabled frames. International Journal of Solids and Structures 1990, Vol. 26:1159-1171. Nos. 9/10.
91. Simitses G.J., Vlahinos A.S. Stability analysis of semi-rigidly connected simple frames. Journal of Constructional Steel Research 1982, Vol. 2(No. 3):29-32.
92. Simitses G.J., Vlahinos A.S. Sway buckling of unbraced multistory frames. Computers and Structures 1986, Vol. 22(No. 6):1047-1054.
93. Simitses G.J., Giri J., Kounadis A.N. Nonlinear analysis of portal frames. International Journal of Numerical Methods in Engineering 1981, Vol. 17:123-132.
94. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1961, McGraw-Hill Book Co, New York.
95. Vlahinos A.S., Smith C.V., Simitses G.J. A nonlinear solution scheme for multistory, multibay plane frames. Computers and Structures 1986, Vol. 22(No. 6):1035-1045.
96. Zimmermann H. Die Knickfestigkeit des geraden Stabes mit mehreren Feldern. Sitzungsberichte der preussischen Akademie der Wissenschaften 1909, 180.
97. Zimmermann H. Die Knickfestigkeit der Druckgurte offener Brücken 1910, W. Ernst and Sohn, Berlin, Germany.
98. Zimmermann H. Die knickfestigkeit der Stabrerbindungen 1925, W. Ernst und Sohn, Berlin, Germany.
99. Finlayson B.A., Scriven L.E. The method of weighted residuals - a review. Appl. Mech. Rev. 1966, Vol. 19(No. 9):735-748.
100. Galerkin B.G. Sterzhnei i plastiny. Ryady V Nekotorykh Voprosakh Uprogogo Ravnoresiya Sterzhnei i plastiny, (Rods and Plates. Series Occuring in Some Problems of Elastic Equilibrium of Rods and Plates). Vesin. Inzhen. i Tekh. Petrograd 1941, Vol. 19:897-908. 1915; English translation 63-18924 Clearinghouse Fed. Sci. Tech. Info. See also.
101. Galerkin B.G. On the Seventieth Anniversary of the Birth of B. G. Galerkin. PMM 1941, Vol. 5:337-341.
102. Hutchinson J.W., Koiter W.T. Postbuckling theory. Appl. Mech. Rev. 1970, Vol. 13:1353-1366.
103. Koiter W.T. Elastic Stability and Postbuckling Behavior. Non-linear Problems 1963, University of Wisconsin Press, Madison. R.E. Langer (Ed.).
104. The Stability of Elastic Equilibrium," Thesis Delft (English translation, NASA TT-F-10833, 1967, and AFFDL TR-70-25, 1970).
105. Prager W., Taylor J.E. Problem of optimal structural design. J. Appl. Mech. 1968, Vol. 35:102-106.
106. Rayleigh J.W.S. Theory of Sound 1945, Dover Publications, New York.
107. Sagan H. Introduction to the Calculus of Variations 1969, McGraw-Hill Book Co., New York.
108. Simitses G.J., Kamat M.P., Smith C.V. The Strongest Column by the Finite Element Displacement Method. AIAA Paper No. 72-141 1972.
109. Singer J. On the equivalence of the galerkin and Rayleigh-Ritz methods. Journal of Royal Aeronautical Society 1962, Vol. 66:592-597.
110. Stein M. Recent Advances in Shell Buckling. AIAA Paper No. 68-103 1968.
111. Tadjbakhsh I., Keller J.B. Strongest columns and isoperimetric inequalities for Eigen values. J. Appl. Mech. 1962, Vol. 29:159-164.
112. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1956, McGraw-Hill Book Co., New York.
113. Trefitz E. Zur Theorie der Stabilität des Elastichen Gleichogewihts. Z. Angew. Math. Mech. 1933, Vol. 13:160-165.
114. Goodier J.N., Hsu C.S. Nonsinusoidal buckling modes of sandwich plates. Journal of Aerospace Science 1954, 525-532. August.
115. Hetenéyi M. Beams on Elastic Foundation 1946, The University of Michigan Press, Ann Arbor.
116. Berdichevsky V.L. Variational Principles of Continum Mechanics 1983, Nauka, Moscow.
117. Berdichevsky V.L., Starosel'skii L.A. On the theory of curvilinear Tinoshenko-type rods. Prikl Matem. Mekham. 1983, 47:809-817.
118. Biezeno C.B. Das Durchschlagen eines Schwach Gekrummten Stabes. Zeitschrift Ange. Math. und Mekh. 1938, Vol. 18:21.
119. Boresi A. A refinement of the theory of buckling of rings under uniform pressure. J. Appl. Mech. 1955, Vol. 22:95-102.
120. Epstein M., Murray D.W. Large deformation in-plane analysis of elastic beams. Computers and Structures 1976, 6:1-9.
121. Franciosi V., Augusti G., Sparacio R. Collapse of arches under repeated loading. J. Struct. Div., ASCE 1964, Vol. 90:165. STI.
122. Fung Y.C., Kaplan A. Buckling of Low Arches or Curved Beams of Small Curvature. NACA TN 2840 1952.
123. Gellin S. The plastic buckling of long cylindrical shells under pure bending. International Journal of Solids and Structures 1980, 16:397-407.
124. Gjelsvik A., Bodner S.R. The energy criterion and snap buckling of arches. J. Eng. Mech. Div., ASCE 1962, Vol. 88:87. EM5.
125. Hodges D.H. Proper definition of curvature in nonlinear beam kinematics. AIAA Journal 1984, 22:1825-1827.
126. Hodges D.H. Non-linear inplane deformation and buckling of rings and high arches. International Journal of Non-Linear Mechanics 1999, 34:723-737.
127. Hodges D.H., Ormiston R.A., Peters D.A. On the nonlinear deformation geometry of Euler-Bernoulli beams. Technical Report TP-1566 NASA 1980, Also AVRADCOM Technical Report 80-A-1.
128. Hoff N.J., Bruce V.G. Dynamic analysis of the buckling of laterally loaded flat arches. J. Math and Phys. 1954, Vol. XXXII(No. 4).
129. Lee H.N., Murphy L.M. Inelastic buckling of shallow arches. J. Eng. Mech. Div., ASCE 1968, Vol. 94:225. EMI.
130. Marguerre K. Die Durchschlagskraft eines Schwach Gekrümmten Balken. Sitz. Berlin Math. Gess. 1938, Vol. 37:92.
131. Masur E.F., Lo D.L.C. The shallow arch-general buckling, post-buckling, and imperfection analysis. J. Struct. Mech. 1972, Vol. 1(No. 1):91.
132. Navier Résumé des Leçons sur L'Application de la Méchanique 1833, 273, Paris. 2nd ed.
133. Onat E.T., Shu L.S. Finite deformation of a rigid perfectly plastic arch. J. Appl. Mech. 1962, Vol. 29(No. 3):549.
134. Reissner E. On one-dimensional finite-strain beam theory: The plane problem. Journal of Applied Mathematics and Physics (ZAMP) 1972, 23:795-804.
135. Roorda J. Stability of structures with small imperfections. J. Eng. Mech. Div., ASCE 1965, Vol. 91:87. EMI.
136. Sanders J.L. Nonlinear theories for thin shells. Quart. Appl. Math 1963, Vol. 21:21-36.
137. Schreyer H.L., Masur E.F. Buckling of shallow arches. J. Eng. Mech. Div., ASCE 1966, Vol. 92:1. EM4.
138. Simitses G.J. Snapping of low pinned arches on an elastic foundation. J. Appl. Mech. 1973, Vol. 40(No. 3):741.
139. Singer J., Babcock C.O. On the buckling of rings under constant directional and centrally directed pressure. J. Appl. Mech. 1970, Vol. 37(No. 1):215-218.
140. Smith C.V., Simitses G.J. Effect of Shear and Load Behavior on Ring Stability. Proc. ASCE 1969, 559-569. EM3.
141. Timoshenko S.P. Buckling of curved bars with small curvature. J. Appl. Mech. 1935, Vol. 2(No. 1):17.
142. Timoshenko S.P., Gere J. Theory of Elastic Stability 1961, 287-293, McGraw-Hill Book Co, New York.
143. Wasserman E. The effect of the behavior of the load on the frequency of free vibrations of a ring 1961, NASA TT-F-52.
144. Wempner G., Kesti N. On the buckling of circular arches and rings. Proceedings, Fourth U.S. National Congress of Applied Mechanics 1962, Vol. 2:843-852. ASME.
145. Ziegler H. Principles of Structural Stability 1968, Blaisdell Publishing Company, Waltham, Massachusetts.
146. Handbook of Mathematical Functions 1970, National Bureau of Standards, Washington, DC. M. Abramowitz, I. Stegun (Eds.).
147. Bauld N.R., Tzeng L.-S. A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections. International Journal of Solids and Structures 1984, 20:277-297.
148. Hodges D.H. Improved approximations via Rayleigh's quotient. Journal of Sound and Vibration 1997, 199:155-164.
149. Hodges D.H. Non-linear inplane deformation and buckling of rings and high arches. International Journal of Non-linear Mechanics 1999, 34:723-737.
150. Hodges D.H., Peters D.A. On the lateral buckling of uniform slender cantilever beams. International Journal of Solids and Structures 1975, 11:1269-1280.
151. Hodges D.H., Peters D.A. Lateral-torsional buckling of cantilevered elastically coupled strip-and I-beams. International Journal of Solids and Structures 2001, 38:1585-1603.
152. Michell A.G.M. Elastic stability of long beams under transverse forces. Philosophical Magazine 1899, 48:298-309.
153. Pandey M., Kabir M., Sherbourne A. Flexural-torsional stability of thin-walled composite I-section beams. Composites Engineering 1995, 5:321-342.
154. Prandtl L. Kipperscheinungen. Doctoral dissertation 1899, Universitat Miinchen.
155. Reissner E. On lateral buckling of end-loaded cantilever beams. Journal of Applied Mathematics and Physics (ZAMP) 1979, 30:31-40.
156. Reissner H. Uber die Stabilitat der Biegung 1904, 53-56. Sitz.-Ber. der Berliner Mathem. Gesellschaft III. Jhg.
157. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1961, McGraw-Hill Book Company, New York. 2nd edition.
158. Volovoi V.V., Hodges D.H., Berdichevsky V.L., Sutyrin V. Asymptotic theory for static behavior of elastic anisotropic I-beams. International Journal of Solids and Structures 1999, 36:1017-1043.
159. Handbook of Mathematical Functions 1970, National Bureau of Standards, Washington, D.C. M. Abramowitz, I. Stegun (Eds.).
160. Bhuta P.G., Jones J.P. On axial vibrations of a whirling bar. The Journal of the Acoustical Society of America 1963, 35.
161. Brunelle E.J. Stress redistribution and instability of rotating beams and disks. AIAA Journal 1971, 9:758-759.
162. Bryson A.E., Ho Y.-C. Applied Optimal Control 1975, Blaisdell Publishing Company, Waltham, Massachusetts.
163. Degener M., Hodges D.H., Petersen D. Analytical and experimental study of beam torsional stiffness with large axial elongation. Journal of Applied Mechanics 1988, 110:171-178.
164. Geer J.F., Andersen C.M. A hybrid perturbation galerkin technique with applications to slender body theory. SIAM Journal of Applied Mathematics 1989, 49:344-361.
165. Hodges D.H. Improved approximations via Rayleigh's quotient. Journal of Sound and Vibration 1997, 199:155-164.
166. Hodges D.H., Bless R.R. Axial instability of rotating rods revisited. International Journal of Non-Linear Mechanics 1994, 29:879-887.
167. Lakin W.D., Nachman A. Vibration and buckling of rotating flexible rods at transitional parameter values. Journal of Engineering Mathematics 1979, 13:339-346.
168. Peters D.A., Hodges D.H. In-plane vibration and buckling of a rotating beam clamped off the axis of rotation in-plane vibration and buckling of a rotating beam clamped off the axis of rotation. Journal of Applied Mechanics 1980, 47:398-402.
169. Barsoum R.S. Finite element method applied to the problem of stability of a nonconservative system. International Journal for Numerical Methods in Engineering 1971, 3:63-87.
170. Beck M. Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes. ZAMP 1952, 3:225-288.
171. Bolotin V.V. On vibrations and stability of bars under the action of non-conservative forces. Kolebaniia v turbomashinakh 1959, 23-42. USSR.
172. Bolotin V.V. Nonconservative Problems of the Theory of Elastic Stability 1963, Pergamon Press, New York.
173. Bolotin V.V. Dynamic Stability of Elastic Systems 1964, Holden-Day, Inc., San Francisco.
174. Celep Z. On the lateral stability of a cantilever beam subjected to a non-conservative load. Journal of Sound and Vibration 1979, 64:173-178.
175. Chen L.-W., Ku D.-M. Eigenvalue sensitivity in the stability analysis of Beck's column with a concentrated mass at the free end. Journal of Sound and Vibration 1992, 153:403-411.
176. Como M. Lateral buckling of a cantilever subjected to a transverse follower force. International Journal of Solids and Structures 1966, 2:515-523.
177. Detinko F.M. Some phenomena for lateral flutter of beams under follower load. International Journal of Solids and Structures 2002, 39:341-350.
178. Herrmann G. Stability of equilibrium of elastic systems subjected to nonconservative forces. Applied Mechanics Reviews 1967, 103-108.
179. Higuchi K. An experimental model of a flexible free-free column in dynamic instability due to an end thrust. Proceedings of the 35th Structures, Structural Dynamics, and Materials Conference 1994, 2402-2408. Hilton Head, South Carolina.
180. Hodges D.H. Finite rotation and nonlinear beam kinematics. Vertica 1987, 11:297-307.
181. Hodges D.H. A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams. International Journal of Solids and Structures 1990, 26:1253-1273.
182. Hodges D.H. Lateral-torsional flutter of a deep cantilever loaded by a lateral follower force at the tip. Journal of Sound and Vibration 2001, 247:175-183.
183. Hodges D.H. Geometrically-exact, intrinsic theory for dynamics of curved and twisted anisotropic beams. AIAA Journal 2003, 41:1131-1137.
184. Hodges D.H. Nonlinear Composite Beam Theory for Engineers 2006, Chapts. 4 and 5, American Institute of Aeronautics and Astronautics, Reston, VA.
185. Langthjem M.A., Sugiyama Y. Dynamic stability of columns subjected to follower loads: a survey. Journal of Sound and Vibration 2000, 238:809-851.
186. Leipholz H.H.E. On the influence of damping on the stability of elastic beams subjected to uniformly distributed compressive forces. Proceedings of the Third Brazilian Congress of Mechanical Engineering 1975.
187. Leipholz H.H.E. On variational principles for non-conservative mechanical systems with follower forces. Variational Methods in the Mechanics of Solids 1978, 151-155. Pergamon Press. S. Nemat-Nasser (Ed.).
188. Park Y.P. Dynamic stability of a free Timoshenko beam under a controlled follower force. Journal of Sound and Vibration 1987, 113:407-415.
189. Wohlhart K. Dynamische Kippstabilität eines Plattenstreifens unter Folgelast. Zeitschrift für Flugwissenschaften 1971, 19:291-298.
190. Ziegler H. Principles of Structural Stability 1968, Blaisdell Publishing Company Waltham, Massachusetts.
191. Fluid Structure Interaction Phenomena in Pressure Vessel and Piping Systems 1977, ASME, New York. M.K. Au-Yang, S.J. Brown (Eds.).
192. Benjamin T.B. Dynamics of a system of articulated pipes conveying fluid. Proc. R. Soc. London Ser. A 1961, 26:452-486.
193. Blevins R.D. Flow-Induced Vibration 1977, Van Nostrand-Reinhold, New York.
194. Bohn M.P., Herrmann G. The dynamic behavior of articulated pipes conveying fluid with periodic flow rate. J. Appl. Mech. 1974, 41(1):55-62.
195. Bolotin V.V., Weingarten V.I. The Dynamic Stability of Elastic Systems 1964, Holden-Day, San Francisco, translated by.
196. Budiansky B. Dynamic buckling of elastic structures: Criteria and estimates. Dynamic Stability of Structures 1967, Pergamon, New York. G. Herrmann (Ed.).
197. Budiansky B., Hutchinson J.W. Dynamic buckling of imperfection-sensitive structures. Proc. XI International Congress of Applied Mechanics 1964, Munich.
198. Budiansky B., Roth R.S. Axisymmetric dynamic buckling of clamped shallow spherical shells 1962, NASA TN D-1510, Collected Papers on Instability of Shell Structures.
199. Chen S.S. Vibration of a row of circular cylinders in a liquid. J. Eng. Ind., Trans. ASME. 1975, 91(4):1212-1218.
200. Chen S.S. Vibration of nuclear fuel bundles. Nucl. Eng. Des. 1975, 35(3):399-422.
201. Chen S.S. Crossflow-induced vibrations of heat exchanger tube banks. Nucl. Eng. Des. 1978, 47(1):67-86.
202. Chen S.S. Fluid damping for circular cylindrical structures. Nucl. Eng. Des. 1981, 63(1):81-100.
203. Crocco L., Cheng S.I. Theory of Combustion Instability in Liquid Propallant Rocket Motors. AGARD Monograph No. 8. 1956, Butterworths, London.
204. Dowell E. Nonlinear flutter of curved plates. AIAA J. 1969, 1(3):424-431. March.
205. Dowell E. Panel flutter, a review of the aeroelastic stability of plates and shells. AIAA J. 1970, 8(3):385-399. March.
206. Ginsberg J.H. The dynamic stability of a pipe conveying a pulsatile flow. Int. J. Eng. Sci. 1973, 11:1013-1024.
207. Gregory R.W., Paidoussis M.P. Unstable oscillation of tubular cantilevers conveying fluid. Prod. R. Soc. London Ser. A 1966, 293:512-527.
208. Herrmann G. Stability of equilibrium of elastic systems subjected to nonconservative forces. Appl. Mech. Rev. 1967, 20(2):103-108. Feb.
209. Herrmann G., Bungay R.W. On the stability of elastic systems subjected to nonconservative forces. J. Appl. Mech. 1964, 31(3):435-440.
210. Hill J.L., Swanson C.P. Effects of lumped masses on the stability of fluid conveying tubes. J. Appl. Mech. 1970, 37(2):494-497.
211. Hoff N.J. Dynamic stability of structures. Dynamic Stability of Structures 1967, Pergamon, New York. G. Herrmann (Ed.).
212. Hoff N.J., Bruce V.C. Dynamic analysis of the buckling of laterally loaded flat arches. Q. Math. Phys. 1954, 32:276-288.
213. Hsu C.S. The effects of various parameters on the dynamic stability of a shallow arch. J. Appl. Mech. 1967, 34(2):349-356.
214. Hsu C.S. Equilibrium configurations of a shallow arch of arbitrary shape and their dynamic stability character. Int. J. Nonlinear Mech. 1968, 3:113-136. June.
215. Hsu C.S. On dynamic stability of elastic bodies with prescribed initial conditions. Int. J. Nonlinear Mech. 1968, 4(1):1-21.
216. Hsu C.S. Stability of shallow arches against snap-through under timewise step loads. J. Appl. Mech. 1968, 35(1):31-39.
217. Hsu C.S., Kuo C.T., Lee S.S. On the final states of shallow arches on elastic foundations subjected to dynamic loads. J. Appl. Mech. 1968, 35(4):713-723.
218. Junger M., Feit D. Sound, Structures and Their Interaction 1972, MIT Press, Cambridge, Mass.
219. King R. A review of vortex shedding research and its applications. Ocean Eng. 1977, 4:141-171.
220. Koning C., Taub J. Impact buckling of thin bars in the elastic range hinged at both ends. Luftfahrtforschung 1933, 10(2):55-64. translated as NACA TM 748 in 1934).
221. Kornecki A. Traveling wave-type flutter of infinite elastic plates. AIAA J. 1970, 1342-1344. 8, 7 July.
222. Kuo G.C., Morino L., Dugundji J. Perturbation and harmonic balance methods of nonlinear panel flutter. AIAA J. 1972, 10(11):1479-1484. Nov.
223. Lefschetz S. Stability of Nonlinear Control of Airplanes and Helicopters 1965, Academic Press, New York.
224. Morino L. Perturbation method for treating nonlinear panel flutter problems. AIAA J. 1969, 7(3):405-411. March.
225. Paidoussis M.P. Dynamics of tubular cantilevers conveying fluid. J. Mech. Sci. 1970, 12(2):85-103.
226. Paidoussis M.P., Deksnis B.E. Articulated models of cantilevers conveying fluid: The study of a paradox. J. Mech. Eng. Sci. 1970, 42(4):288-300.
227. Paidoussis M.P., Issid N.T. Experiments on parametric resonance of pipes containing pulsatile flow. J. Appl. Mech., Trans. ASME 1976, 98:198-202.
228. Paidoussis M.P., Sundararajan C. Parametric and combination resonances of a pipe conveying pulsating fluid. J. Appl. Mech. 1975, 42(4):780-784.
229. Reusselet J., Herrmann G. Flutter of articulated pipes at finite amplitude. Trans. ASME 1977, 99(1):154-158.
230. Routh E.J. Stability of Motion 1975, Originally it appeared in 1877, Taylor & Francis, Halsted Press, New York. A.T. Fuller (Ed.).
231. Scanlan R.H., Simin E. Wind Effects on Structures: An Introduction to Wind Engineering 1978, Wiley, New York.
232. Seckel E. Stability and Control of Airplanes and Helicopters 1964, Academic Press, New York.
233. Simitses G.J. Dynamic snap-through buckling of low arches and shallow spherical caps. June Ph.D. Dissertation 1965, Department of Aeronautics and Astronautics, Stanford University.
234. Simitses G.J. On the dynamic buckling of shallow spherical caps. J. Appl. Mech. 1974, (1):299-300. 1974.
235. Simitses G.J. Dynamic Stability of Suddenly Loaded Structures 1989, Springer-Verlag, New York.
236. Stoker J.J. Non-Linear Vibrations in Mechanical and Electrical Systems 1950, vol. II. Interscience, London.
237. Stoker J.J. On the stability of mechanical systems. Commun. Pure Appl. Math. 1955, VIII:133-142.
238. Tamura Y.S., Babcock C.D. Dynamic stability of cylindrical shells under step loading. J. Appl Mech. 1975, 42(1):190-194.
239. Thompson J.M.T. Dynamic buckling under step loading. Dynamic Stability of Structures 1967, Pergamon, New York. G. Herrmann (Ed.).
240. Thompson W., Tait P.G. Treatise on Natural Philosophy 1923, part I, It was first published in 1867, Cambridge University Press, Cambridge, England.
241. Wauer J. Uber Kinetische Verweigungs Probleme Elasticher Strukturen unter Stosseblastung. Ingenieur-Arch. 1980, 49:227-233.
242. Ziegler H. On the concept of elastic stability. Advances in Applied Mechanics 1956, vol. 4:351-403. Academic Press, New York.
243. Ziegler H. Principles of Structural Stability 1968, Blaisdell, Waltham, Mass.
244. Argyris J.H., Kelsey S. Energy Theorems and Structural Analysis 1960, Butterworth Scientific Publications, London.
245. Berg P.W. Calculus of Variations. Handbook of Engineering Mechanics 1962, Ch. 16, McGraw-Hill Book Co, New York. W. Flügge (Ed.).
246. Carslaw H.S. Introduction to the Theory of Fourier's Series and Integrals 1930, Dover Publications, Inc, New York.
247. Courant R., Hilbert D. Methods of Mathematical Physics 1953, Vol. 1. Interscience Publishers, New York.
248. Dym C.L., Shame I.H. Solid Mechanics: A Variational Approach 1973, McGraw-Hill Book Co, New York.
249. Franklin P. Basic Mathematical Formulas. Fundamental Formulas of Physics 1960, Dover Publications, Inc, New York. D.H. Menzel (Ed.).
250. Fung Y.C. Foundations of Solid Mechanics 1965, Prentice-Hall, Inc., Englewood Cliffs, N. J.
251. Gelfand I.M., Fomin S.V. Calculus of Variations 1963, Translated from the Russian, Prentice-Hall, Inc, Englewood Cliffs, N. J. R.A. Silverman (Ed.).
252. Hoff N.J. The Analysis of Structures 19560, John Wiley & Sons, Inc, New York.
253. Kantorovich L.V., Krylov V.I. Approximate Methods of Higher Analysis 1958, translated from the Russian by C. D. Benster, Interscience Publishers, New York. 4th ed.
254. Langhaar H.L. Energy Methods in Applied Mechanics 1962, John Wiley & Sons, Inc., New York.
255. Oden J.T. Mechanics of Elastic Structures 1967, McGraw-Hill Book Co, New York.
256. Pestel E.C., Leckie F.A. Matrix Methods in Elastomechanics 1963, McGraw-Hill Book Co, New York.
257. Phillips E.G. Functions of a Complex Variable with Applications 1954, Oliver and Boyd, London.
258. Przemieniecki J.S. Theory of Matrix Structural Analysis 1968, McGraw-Hill Book Co, New York.
259. Rayleigh J.W.S. Theory of Sound 1945, Dover Publications, Inc., New York.
260. Ritz W. Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physic. J. Reine Angew. Math. 1909, Vol. 135:1-61.
261. Timoshenko S.P., Gere J.M. Theory of Elastic Stability 1961, McGraw-Hill Book Co., New York.