Recent research on vibration of structures using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method

Shock and Vibration Digest

Volumn 31, Issue 3, 1999, Pages 187-194

  Chakraverty, S ^a,b   Bhat, R B ^a   Stiharu, I ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b CSIR CENTRAL BUILDING RESEARCH INSTITUTE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; POLYNOMIALS; STRUCTURAL ANALYSIS;

BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS; RAYLEIGH-RITZ METHOD;

VIBRATIONS (MECHANICAL);

EID: 0032627155     PISSN: 05831024     EISSN: None     Source Type: Journal    
DOI: 10.1177/058310249903100301     Document Type: Article

References (154)

1. Askey, R. A., 1975, Orthogonal Polynomials and Special Functions, Society for Industrial and Applied Mathematics, Philadelphia.
2. Auciello, N. M., and Maurizi, M. J., 1997, "On the Natural Vibrations of Tapered Beams with Attached Inertia Elements," Journal of Sound and Vibration, Vol. 199, No. 3, 522-530.
3. Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice Hall, Englewood Cliffs, New Jersey.
4. Bert, C. W., 1976, "Dynamics of Composite and Sandwich Panels - Parts I and II," Shock and Vibration Digest, Vol. 8, 37-48, 15-24.
5. Bert, C. W., 1979, "Recent Research in Composite and Sandwich Plate Dynamics," Shock and Vibration Digest, Vol. 11, 13-23.
6. Bert, C. W., 1980, "Recent Advances in Structural Dynamics," in Proceedings of the Vibration of Composite Structures, Vol. 2, Southampton, England, 693-712.
7. Bert, C. W., 1982, "Research on Dynamics of Composite and Sandwich Plates," Shock and Vibration Digest, Vol. 14, 17-34.
8. Bert, C. W., 1985, "Research on Dynamic Behavior of Composite and Sandwich Plates - IV," Shock and Vibration Digest, Vol. 17, 3-15.
9. Bert, C. W., 1991, "Research on Dynamic Behavior of Composite and Sandwich Plates - V: Part I," Shock and Vibration Digest, Vol. 23, 3-14.
10. Bhat, R. B., 1985a, "Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 102, No. 4, 493-499.
11. Bhat, R. B., 1985b, "Plate Deflections Using Orthogonal Polynomials," Journal of Engineering Mechanics, Trans. ASCE, Vol. 111, No. 11, 1301-1309.
12. Bhat, R. B., 1985c, "Vibration of Rectangular Plates Using Beam Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," in Proceedings of the 3rd International Modal Analysis Conference, Orlando, Florida.
13. Bhat, R. B., 1985d, "Vibration of Structures Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," in Proceedings of the 10th Canadian Congress of Applied Mechanics, London, Ontario.
14. Bhat, R B., 1986a, "Transverse Vibrations of a Rotating Uniform Cantilever Beam with Tip Mass as Predicted by Using Beam Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 105, No. 2, 199-210.
15. Bhat, R. B. 1986b, "Beam Characteristics Using Orthogonal Polynomials with Fractional Power Increments," Journal of Sound and Vibration, Vol. 112, No. 3, 556-558.
16. Bhat, R. B , 1986c, "Natural Frequencies of Triangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," in Proceedings of the Symposium on Recent Trends in Aeroelasticity, Structures and Structural Dynamics, Gainesville.
17. Bhat, R. B., 1986d, "Natural Frequencies of Rectangular-Plates with Free Edges - Comments," Journal of Sound and Vibration, Vol. 111, No. 1, 171-172.
18. Bhat, R. B., 1986e, "Application of Rayleigh-Ritz Method on the Finite Element Model of a Structure as a Means of Coordinate Reduction," Journal of Sound and Vibration, Vol. 108, No. 2, 355-356.
19. Bhat, R. B., 1986f, "Author's Reply on - Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 108, No. 2, 353-354.
20. Bhat, R. B., 1986g, "Author's Reply on - Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 108, No. 1, 167-168.
21. Bhat, R. B., 1987a, "Flexural Vibration of Polygonal Plates Using Characteristic Orthogonal Polynomials in Two Variables," Journal of Sound and Vibration, Vol. 114, No. 1, 65-71.
22. Bhat, R. B., 1987b, "Rayleigh-Ritz Method with Separable Deflection Expressions for Structural Segments," Journal of Sound and Vibration, Vol. 115, No. 1, 174-177.
23. Bhat, R. B., 1989, "Natural Frequencies of Edge Restrained Tapered Plates Using Boundary Characteristic Orthogonal Polynomials," in Proceedings of the Twelfth Biennial ASME Conference on Mechanical Vibration and Noise, Montreal, Canada, 113-117.
24. Bhat, R. B., 1991a, "Acoustics of a Cavity-Backed Membrane - The Indian Musical Drum," Journal of the Acoustical Society of America, Vol. 90, No. 3, 1469-1474.
25. Bhat, R. B., 1991b, "Vibration of Rectangular-Plates on Point and Line Supports Using Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 149, No. 1, 170-172.
26. Bhat, R. B., 1997, "Nature of Stationarity of the Natural Frequencies at the Natural-Modes in the Rayleigh-Ritz Method." Journal of Sound and Vibration, Vol. 203, No. 2, 251-263.
27. Bhat, R. B., Chakraverty, S., and Stiharu, I., 1998, "Recurrence Scheme for the Generation of Two Dimensional Boundary Characteristic Orthogonal Polynomials to Study Vibration of Plates," Journal of Sound and Vibration, U.K., Vol. 216, No. 2, 321-327.
28. Bhat, R. B., Laura, P A.A., Gutierrez, R. G., Cortinez, V. H., and Sanzi, H. C., 1990, "Numerical Experiments on the Determination of Natural Frequencies of Transverse Vibrations of Rectangular Plates of Non-Uniform Thickness," Journal of Sound and Vibration, Vol. 138, 205-219.
29. Bhat, R. B., and Mundkur, G., 1993, "Vibration of Plates Using Plate Characteristic Functions Obtained by Reduction of Partial-Differential Equation," Journal of Sound and Vibration, Vol. 161, No. 1, 157-171.
30. Chakraverty, S., 1992, "Numerical Solution of Vibration of Plates," Ph.D. thesis, University of Roorkee, Roorkee, India.
31. Chakraverty, S., 1996a, "Efficient Method for Finding Deflection of Circular and Elliptic Plates," Journal of Institution of Engineers, India, Vol. 77, 7-11.
32. Chakraverty, S., 1996b, "Effect of Orthotropy on Natural Frequencies of Vibration of Elliptic Plates," in Proceedings of the Conference on Mathematics and Its Applications in Engineering and Industry, Department of Mathematics, University of Roorkee, Roorkee, India.
33. Chakraverty, S., 1996c, "An Efficient Numerical Technique for Finding Natural Frequencies of Free Orthotropic Elliptic Plates," in Proceedings of the 3rd International Conference on Vibration Problems, University of North Bengal, India.
34. Chakraverty, S., and Chakrabarti, S. C., 1993, "Deflection of a Circular Plate Using Orthogonal Polynomials," in Proceedings of the Indian Society of Industrial and Applied Mathematics Conference, Roorkee University, India.
35. Chakraverty, S., and Petyt, M., 1996, "Free Vibration of Nonhomogeneous Elliptic Plates Using Boundary Characteristic Orthogonal Polynomials," in Proceedings of the European Space Agency, International Workshop on Advanced Mathematics in the Dynamics of Flexible Bodies, ESA-ESTEC, Noordwijk, the Netherlands.
36. Chakraverty, S., and Petyt, M., 1997a, "Natural Frequencies for Free Vibration of Non-Homogeneous Elliptic and Circular Plates Using Two Dimensional Orthogonal Polynomials," Applied Mathematical Modeling, Vol. 21, 399-417.
37. Chakraverty, S., and Petyt, M., 1997b, "Transverse Vibration of Orthotropic Elliptic Plates Using Orthogonal Polynomials in the Rayleigh-Ritz Method," in Proceedings of the 6th International Conference on Recent Advances in Structural Dynamics, Institute of Sound and Vibration Research, University of Southampton, United Kingdom.
38. Chakraverty, S., and Petyt, M., 1998, "Free Vibration Analysis of Elliptic and Circular Plates Having Rectangular Orthotropy," International Journal of Structural Engineering and Mechanics, accepted for publication.
39. Chihara, T. S., 1978, An Introduction to Orthogonal Polynomials, Gordon and Breach, London.
40. Cupial, P., 1997, "Calculation of the Natural Frequencies of Composite Plates the Rayleigh-Ritz Method with Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 201, No. 3, 385-387.
41. Dickinson, S M., and Di Blasio, A., 1986, "On the Use of Orthogonal Polynomials in the Rayleigh-Ritz Method for the Study of the Flexural Vibration and Buckling of Isotropic and Orthotropic Rectangular Plates," Journal of Sound and Vibration, Vol. 108, No. 1, 51-62
42. Frederiksen, P S., 1995, "Single-Layer Plate Theories Applied to the Flexural Vibration of Completely Free Thick Laminates," Journal of Sound and Vibration, Vol. 186, No. 5, 743-759.
43. Freud, G., 1971, Orthogonal Polynomials, Pergamon Press, Oxford, United Kingdom.
44. Geannakakes, G. N, 1988, "A Theoretical Formulation for the Natural Frequency, Buckling, and Deflection Analysis of Plates Using Natural Coordinates and Characteristic Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 124, No. 2, 385-387.
45. Geannakakes, G. N., 1990, "Vibration Analysis of Arbitrarily Shaped Plates Using Beam Characteristic Orthogonal Polynomials in the Semianalytical Finite Strip Methods," Journal of Sound and Vibration, Vol. 137, No. 2, 283-303.
46. Geannakakes, G. N., 1995, "Natural Frequencies of Arbitrarily-Shaped Plates Using the Rayleigh-Ritz Method Together with Natural Coordinate Regions and Normalized Characteristic Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 182, No. 3, 441-478.
47. German, D. J., 1975, Free Vibration Analysis of Beams and Shafts, John Wiley, New York.
48. Gorman, D. J., 1982, Free Vibration Analysis of Rectangular Plates, Elsevier, North-Holland, Amsterdam.
49. Grossi, R. O., and Albarracin, C. M., 1998, "A Variant of the Method of Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 212, No. 4, 749-752.
50. Grossi, R. O., Aranda, A., and Bhat, R. B., 1993, "Vibration of Tapered Beams with One End Spring Hinged and the Other End with Tip Mass," Journal of Sound and Vibration, Vol. 160, No. 1, 175-178.
51. Grossi, R. O., and Bhat, R. B., 1991, "A Note on Vibrating Tapered Beams" Journal of Sound and Vibration, Vol. 147, No. 1, 174-178.
52. Grossi, R. O., and Bhat, R. B., 1995, "Natural Frequencies of Edge Restrained Tapered Rectangular-Plates," Journal of Sound and Vibration, Vol. 185, No. 2, 335-343.
53. Kaushal, A., and Bhat, R. B., 1988, "Lateral Vibrations of Rotating Cantilever Beams Using Beam Characteristic Polynomials in Reissner Method," in Proceedings of the 2nd International Symposium on Transport Phenomena, Dynamics and Design of Rotating Machinery, Honolulu, Hawaii.
54. Kaushal, A., and Bhat, R. B., 1989a, "Tangential Velocity Effect on the Dynamic Behaviour of Turbine Blades," in Proceedings of the 12th Biennial ASME Conference on Mechanical Vibration and Noise, Montreal, Canada.
55. Kaushal, A., and Bhat, R. B., 1989b, "Axisymmetric Vibrations of Rotating Circular Plates Using Characteristic Orthogonal Polynomials," in Proceedings of 12th Canadian Congress of Applied Mechanics, Ottawa, Canada.
56. Kim, C. S., 1986, "Comment on Natural Frequencies of Rectangular-Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method - Comment," Journal of Sound and Vibration, Vol. 108, No. 1, 166-168.
57. Kim, C. S., 1988, "The Vibration of Beams and Plates Studied Using Orthogonal Polynomials," Ph.D. thesis, the University of Western Ontario.
58. Kim, C. S., and Dickinson, S. M., 1987a, "The Flexural Vibration of Rectangular-Plates with Point Supports," Journal of Sound and Vibration, Vol. 117, No. 2, 249-261.
59. Kim, C. S., and Dickinson, S. M., 1987b, "The Flexural Vibration of Line Supported Rectangular Plate Systems," Journal of Sound and Vibration, Vol. 114, No. 1, 129-142.
60. Kim, C. S., and Dickinson, S. M., 1988, "On the Analysis of Laterally Vibration Slender Beams Subject to Various Complicating Effects," Journal of Sound and Vibration, Vol. 122, No. 3, 441-455.
61. Kim, C. S., and Dickinson, S. M., 1989a, "On the Free Transverse Vibration of Annular and Circular, Thin, Sectorial Plates Subject to Certain Complicating Effects," Journal of Sound and Vibration, Vol. 134, No. 3, 407-421.
62. Kim, C. S., and Dickinson, S M., 1989b, "On the Lateral Vibration of Thin Annular and Circular Composite Plates Subject to Certain Complicating Effects," Journal of Sound and Vibration, Vol. 130, No. 3, 363-377.
63. Kim, C. S., and Dickinson, S. M., 1989c, "On the Analysis of Laterally Vibrating, Elastically Supported, Slender Beams," Journal of Sound and Vibration, Vol. 129, No. 1, 161-165.
64. Kim, C. S , and Dickinson, S. M., 1990, "The Flexural Vibration of Thin Isotropic and Polar Orthotropic Annular and Circular Plates with Elastically Restrained Peripheries," Journal of Sound and Vibration, Vol. 143, No. 1, 171-179.
65. Kim, C. S., Young, P. G., and Dickinson, S. M., 1990, "On the Flexural Vibration of Rectangular-Plates Approached by Using Simple Polynomials in the Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 143, No. 3, 379-394.
66. Kitipornchai, S., Liew, K. M., Xiang, Y., and Wang, C. M., 1993, "Free Vibration of Isosceles Triangular Mindlin Plates," International Journal of Mechanical Sciences, Vol. 35, No. 2, 89-102.
67. Kuttler, J. R., 1996, "On Flexural Vibration of Skew Plates Using Boundary Characteristic Orthogonal Polynomials in two Variables," Journal of Sound and Vibration, Vol. 194, No. 3, 461-462.
68. Lam, K. Y., Chow, S. T., and Hung, K. C., 1988, "Use of Partitioning and Orthogonal Polynomials for Flexural Vibration of Rectangular Plates," Mechanical Engineering Report RP 637-86-2, National University of Singapore.
69. Lam, K. Y., and Hung, K. C., 1988, "Use of Orthogonal Polynomials and Sub-Sectioning for Flexural Vibration of Plates with Crack and Cutout," Mechanical Engineering Report RP 637-86-1, National University of Singapore.
70. Lam, K. Y., and Hung, K. C., 1990, "Orthogonal Polynomials and Sub-Sectioning Method for Vibration of Plates," Computers and Structures, Vol. 34, No. 6, 827-834.
71. Lam, K Y., and Hung, K. C., 1990b, "Vibration Study on Plates with Stiffened Opening Using Orthogonal Polynomials and Partitioning Method," Computers and Structures, Vol. 37, 295-301.
72. Lam, K. Y., Hung K. C , and Chow, S.T., 1989, "Vibration Analysis of Plates with Cutouts by the Modified Rayleigh-Ritz," Applied Acoustics, Vol. 28, 49-60.
73. Lam, K. Y., and Liew, K. M., 1992, "A Numerical Model Based on Orthogonal Plate Functions for Vibration of Ring Supported Elliptic Plates," Comput. Mech., Vol. 9, 113.
74. Lam, K. Y., Liew, K. M., and Chow, S. T., 1990, "Free Vibration Analysis of Isotropic and Orthotropic Triangular Plates," International Journal of Mechanical Sciences, Vol. 32, No. 5, 455-464.
75. Lam, K. Y., Liew, K. M., and Chow, S. T., 1992, "Use of Two Dimensional Orthogonal Polynomials for Vibration of Circular and Elliptic Plates," Journal of Sound and Vibration, Vol. 154, 261-270.
76. Laura, P.A.A., 1986, "Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method - Comments," Journal of Sound and Vibration, Vol. 108, No. 2, 353-353.
77. Laura, P.A.A., and Ercoli, L., 1993, "Comments on Transverse Vibration of Simply Supported Elliptic and Circular Plates Using Boundary Characteristic Orthogonal Polynomials in Two Variables and Some Additional Considerations," Journal of Sound and Vibration, Vol. 164, No. 1, 188-190.
78. Laura, P.A.A., Gutierrez, R. H., and Bhat, R. B , 1989, "Transverse Vibrations of a Trapezoidal Cantilever Plate of Variable Thickness," AIAA Journal, Vol. 27, No. 7, 921-922.
79. Lee, H. P., and Ng, T. Y., 1994, "Inplane Vibration of Planar Frame Structures," Journal of Sound and Vibration, Vol. 172, No. 3, 420-427.
80. Leissa, A. W., 1969, Vibration of Plates, NASA SP160, U.S. Government Printing Office, Washington, DC.
81. Leissa, A. W., 1977, "Recent Research in Plate Vibrations, 1973-1976: Classical Theory," Shock and Vibration Digest, Vol. 9, No. 10, 13-24.
82. Leissa, A. W., 1978, "Recent Research in Plate Vibrations: 1973-76: Complicating Effects," Shock and Vibration Digest, Vol. 9, No. 11, 21-35.
83. Leissa, A. W., 1981a, "Plate Vibration Research 1976-1980: Classical Theory," Shock and Vibration Digest, Vol. 13, No. 9, 11-22.
84. Leissa, A. W., 1981b, "Plate Vibration Research, 1976-80: Complicating Effects," Shock and Vibration Digest, Vol. 13, No. 10, 19-36.
85. Leissa, A. W., 1987a, "Recent Studies in Plate Vibrations: 1981-1985, Part I. Classical Theory," Shock and Vibration Digest, Vol. 19, No 2, 11-18.
86. Leissa, A. W., 1987b, "Recent Studies in Plate Vibrations: 1981-85, Part II. Complicating Effects," Shock and Vibration Digest, Vol. 19, No. 3, 10-24.
87. Liew, K. M., 1990, "The Development of 2-D Orthogonal Polynomials for Vibration of Plates," Ph.D. thesis, National University of Singapore, Singapore.
88. Liew, K. M., 1992a, "Response of Plates of Arbitrary Shape Subject to Static Loading," Journal of Engineering Mechanics - ASCE, Vol. 118, No. 9, 1783-1794.
89. Liew, K. M., 1992b, "Vibration of Symmetrically Laminated Cantilever Trapezoidal Composite Plates," International Journal of Mechanical Sciences, Vol 34, 299.
90. Liew, K. M., 1992c. "Vibration of Eccentric Ring and Line Supported Circular Plates Carrying Concentrated Masses," Journal of Sound and Vibration, Vol. 156, 99-107.
91. Liew, K. M., 1992d, "Frequency Solutions for Circular Plates with Internal Supports and Discontinuous Boundaries," International Journal of Mechanical Sciences, Vol. 34, 511.
92. Liew, K. M., 1996, "Solving the Vibration of Thick Symmetrical Laminates by Reissner/Mindlin Plate-Theory and the P-Ritz Method," Journal of Sound and Vibration, Vol. 198, No. 3, 343-360.
93. Liew, K. M., Hung, K. C., and Lam, K. Y., 1993, "On the Use of the Substructure Method for Vibration Analysis of Rectangular-Plates with Discontinuous Boundary-Conditions," Journal of Sound and Vibration, Vol. 163, No. 3, 451-462.
94. Liew, K. M., Hung, K. C., and Lim, M. K., 1993a. "A Continuum 3-Dimensional Vibration Analysis of Thick Rectangular-Plates," International Journal of Solids and Structures, Vol. 30, No. 24, 3357-3379.
95. Liew, K. M., Hung, K. C., and Lim, M. K., 1993b, "Roles of Domain Decomposition Method in Plate Vibrations - Treatment of Mixed Discontinuous Periphery Boundaries," International Journal of Mechanical Sciences, Vol. 35, No. 7, 615-632.
96. Liew, K. M., Hung, K. C., and Lim, M K., 1994, "On the Use of the Domain Decomposition Method for Vibration of Symmetrical Laminates Having Discontinuities at the Same Edge," Journal of Sound and Vibration, Vol. 178, No. 2, 243-264.
97. Liew, K. M., Hung, K. C., and Lim, M. K., 1995, "Vibration of Mindlin Plates Using Boundary Characteristic Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 182, 77-90.
98. Liew, K. M., and Lam, K. Y., 1989, "Frequencies and Mode Shapes of Skew Plates," Mechanical Engineering Report RP 637-86-7, National University of Singapore.
99. Liew, K. M., and Lam, K. Y., 1990, "Application of 2-Dimensional Orthogonal Plate Function to Flexural Vibration of Skew Plates," Journal of Sound and Vibration, Vol. 139, No. 2, 241-252.
100. Liew, K. M., and Lam, K. Y., 1991a, "A Rayleigh-Ritz Approach to Transverse Vibration of Isotropic and Anisotropic Trapezoidal Plates Using Orthogonal Plate Functions," International Journal of Solids and Structures, Vol. 27, No. 2, 189-203.
101. Liew, K. M., and Lam, K. Y., 1991b, "A Set of Orthogonal Plate Functions for Vibration Analysis of Regular Polygonal Plate," ASME Journal of Vibration and Acoustics, Vol. 113, 182.
102. Liew, K. M., and Lam, K. Y., 1991c, "Vibration Analysis of Multi-Span Plates Having Orthogonal Straight Edges," Journal of Sound and Vibration, Vol. 147, 255.
103. Liew, K. M., and Lam, K. Y., 1993, "On the Use of 2D-Orthogonal Polynomials in the Rayleigh Ritz Method for Flexural Vibration of Annular Sector Plates of Arbitrary Shape," International Journal of Mechanical Sciences, Vol. 35, No. 2, 129-139.
104. Liew, K. M., Lam, K. Y., and Chow, S. T., 1989, "Study on Flexural Vibration of Triangular Composite Plates Influenced by Fibre Orientation," Composite Structures, Vol. 13, 123-132.
105. Liew, K. M., Lam, K. Y., and Chow, S. T., 1990, "Free Vibration Analysis of Rectangular Plates Using Orthogonal Plate Function," Computers and Structures, Vol. 34, No. 1, 79-85.
106. Liew, K. M., and Lim, C. W., 1994, "Vibratory Characteristics of Cantilevered Rectangular Shallow Shells of Variable Thickness," AIAA Journal.
107. Liew, K. M., Lim, C. W., and Ong, L. S., 1994, "Flexural Vibration of Doubly-Tapered Cylindrical Shallow Shells," International Journal of Mechanical Sciences, Vol. 36, No. 6, 547-565.
108. Liew, K. M., and Wang, C. M., 1992a, "pb-2 Rayleigh-Ritz Method for General Plate Analysis," Engineering Structures, Vol. 14.
109. Liew, K. M., and Wang, C. M., 1992b, "Elastic Buckling of Rectangular Plates with Curved Internal Supports," ASCE Journal of Structural Engineering, Vol. 118, 1480-1493.
110. Liew, K. M., Xiang, Y., Wang, C. M., and Kitipornchai, S., 1993, "Vibration of Thick Skew Plates Based on Mindlin Shear Deformation Plate Theory," Journal of Sound and Vibration, Vol. 164.
111. Lim, C. W., and Liew, K. M., 1994, "A pb-2 Ritz Formulation for Flexural Vibration of Shallow Cylindrical Shells of Rectangular Planform," Journal of Sound and Vibration.
112. Mattei, P. O., 1996, "A 2-Dimensional Chebyshev Collocation Method for the Study of the Vibration of a Baffled Fluid-Loaded Rectangular Plate," Journal of Sound and Vibration, Vol. 196, No. 4, 407-427.
113. Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan, New York.
114. Meirovitch, L., 1986, Elements of Vibration Analysis, 2nd Ed., McGraw-Hill, New York.
115. Mizusawa, T., 1986, "Natural Frequencies of Rectangular Plates with Free Edges," Journal of Sound and Vibration, Vol. 105, 451-459.
116. Mundkur, G., Bhat, R. B., and Neriya, S., 1994, "Vibration of Plaies with Cutouts Using Boundary Characteristic Orthogonal Polynomial Functions in the Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 176, No. 1, 136-144.
117. Muthukumaran, P., Bhat, R. B., and Stiharu, I., 1998, "Localization of Structural Vibration and Acoustic Radiation through Boundary Conditioning," in Proceedings of the CSME Forum SCGM, Ryerson Polytechnic University, Toronto, Canada, 17-23.
118. Muthukumaran, P., Stiharu, I., and Bhat, R. B., 1997, "Vibration of Micromachined Condenser Microphone Plate Diaphragms in Electrostatic Fields," in Proceedings of the 16th Canadian Congress of Applied Mechanics, Quebec, Canada, 87-88.
119. Oosterhout, G. M., Vanderhoogt, P.J.M., and Spiering R.M.E.J., 1995, "Accurate Calculation Methods for Natural Frequencies of Plates with Special Attention to the Higher Modes," Journal of Sound and Vibration, Vol. 183, No. 1, 33-47.
120. Pandey, M. D., and Sherbourne, A. N., 1991, "Buckling of Anisotropic Composite Plates under Stress Gradient," Journal of Engineering Mechanics - ASCE, Vol. 117, No. 2, 260-275.
121. Pandey, M. D., and Sherbourne, A. N., 1992, "Mechanics of Shape Optimization in Plate Buckling," Journal of Engineering Mechanics - ASCE, Vol. 118, No. 6, 1249-1266.
122. Pandey, M. D., and Sherbourne, A. N., 1993, "Stability Analysis of Inhomogeneous, Fibrous Composite Plates," International Journal of Solids and Structures, Vol. 30, No. 1, 37-60.
123. Petyt, M., 1990, Introduction of Finite Element Vibration Analysis, Cambridge University Press, Cambridge, United Kingdom.
124. Petyt, M., and Chakraverty, S., 1997, "Free Vibration of Nonhomogeneous Elliptic Plates," in Proceeding of 16th Canadian Congress of Applied Mechanics, CANCAM 97, Laval University, Quebec City, Canada.
125. Rajalingham, C., and Bhat, R. B., 1991, "Vibration of Elliptic Plates Using Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method," International Journal of Mechanical Sciences, Vol. 33, No. 9, 705-716.
126. Rajalingham, C., and Bhat, R. B., 1993, "Axisymmetrical Vibration of Circular Plates and Its Analog in Elliptic Plates Using Characteristic Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 161, No. 1, 109-118.
127. Rajalingham, C., Bhat, R. B., and Xistris, G. D., 1991, "Natural Frequencies and Mode Shapes of Elliptic Plates with Boundary Characteristic Orthogonal Polynomials as Assumed Shape Functions," in Proceedings of the 13th Biennial Conference on Mechanical Vibration and Noise, Miami, Florida.
128. Rajalingham, C., Bhat, R. B., and Xistris, G. D., 1993, "Natural Frequencies and Mode Shapes of Elliptic Plates with Boundary Characteristic Orthogonal Polynomials as Assumed Shape Functions," ASME Journal of Vibration Acoustics, Vol. 115, 353-358
129. Schmidt, R., 1981, "A Variant of the Rayleigh-Ritz Method," Journal of the Industrial Mathematics Society, Vol. 31, 37-46.
130. Shames, I. H., and Dyms, C. L., 1985, Energy and Finite Element Methods in Structural Mechanics, McGraw-Hill, New York.
131. Singh, B., and Chakraverty, S., 1991, "Transverse Vibration of Completely Free Elliptic and Circular Plates Using Orthogonal Polynomials in Rayleigh-Ritz Method," International Journal of Mechanical Sciences, Vol. 33, No. 9, 741-751.
132. Singh, B , and Chakraverty, S., 1992a, "Transverse Vibration of Triangular Plates Using Characteristic Orthogonal Polynomials in Two Variables," International Journal of Mechanical Sciences, Vol. 34, No. 12, 947-955.
133. Singh, B., and Chakraverty, S., 1992b, "Transverse Vibration of Simply-Supported Elliptic and Circular Plates Using Boundary Characteristic Orthogonal Polynomials in Two Dimensions," Journal of Sound and Vibration, Vol. 152, No. 1, 149-155.
134. Singh, B., and Chakraverty, S., 1992c, "On the Use of Orthogonal Polynomials in Rayleigh-Ritz Method for the Study of Transverse Vibration of Elliptic Plates," International Journal of Computers and Structures, Vol. 43, No. 3, 439-443.
135. Singh, B., and Chakraverty, S., 1993a, "Transverse Vibration of Annular Circular and Elliptic Plates Using Characteristic Orthogonal Polynomials in Two Dimensions," Journal of Sound and Vibration, Vol. 162, No. 3, 537-546.
136. Singh, B., and Chakraverty, S., 1993b, "Transverse Vibration of Simply Supported Elliptic and Circular Plates Using Boundary Characteristic Orthogonal Polynomials in Two Variables - Authors' Reply," Journal of Sound and Vibration, Vol. 164, No. 1, 191-192.
137. Singh, B., and Chakraverty, S., 1994a, "Boundary Characteristic Orthogonal Polynomials in Numerical Approximation," Communications in Numerical Methods in Engineering, Vol. 10, 1027-1043.
138. Singh, B., and Chakraverty, S., 1994b, "Flexural Vibration of Skew Plates Using Characteristic Orthogonal Polynomials in Two Variables," Journal of Sound and Vibration, Vol. 173, No. 2, 157-178.
139. Singh, B., and Chakraverty, S , 1994c, "Use of Characteristic Orthogonal Polynomials in Two Dimensions for Transverse Vibrations of Elliptic and Circular Plates with Variable Thickness," Journal of Sound and Vibration, Vol. 173, No. 3, 289-299.
140. Soedel, W., 1981, Vibration of Shells and Plates, Marcel Dekker, Hong Kong.
141. Steinmann, R., Friemann, H., Prescher, C., and Schellin, R., 1995, "Mechanical-Behavior of Micromachined Sensor Membranes Under Uniform External-Pressure Affected by Inplane Stresses Using a Ritz Method and Hermite-Polynomials," Sensors and Actuators A-Physical, Vol. 48, No. 1, 37-46.
142. Stiharu, I., and Bhat, R. B., 1997, "Vibration of Micro Plates in Electrostatic Fields Using Rayleigh-Ritz Method," in Proceedings of the 15th International Modal Analysis Conference, Orlando, Florida, 765-770.
143. Szego, G., 1967, Orthogonal Polynomials, 3rd Ed., American Mathematical Society, New York.
144. Szilard, R., 1974, Theory and Analysis of Plates: Classical and Numerical Methods, Prentice Hall, Englewood Cliffs, New Jersey.
145. Timoshenko, S., and Woinowsky, K. S., 1959, Theory of Plates and Shells, McGraw-Hill, New York.
146. Tomioka, T., Kobayashi, Y., and Yamada, G., 1996, "Analysis of Free-Vibration of Rotating Disk-Blade Coupled Systems by Using Artificial Springs and Orthogonal Polynomials," Journal of Sound and Vibration, Vol. 191, No. 1, 53-73.
147. Wang, C. M., and Thevendran, V., 1993, "Vibration Analysis of Annular Plates with Concentric Supports Using a Variant of Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 163, No. 1, 137-149.
148. Wendroff, B., 1961, "On Orthogonal Polynomials," American Mathematical Society, Vol. 12, 554-555.
149. Wu, J. R., and Liu, W. H., 1988, "Vibration of Rectangular-Plates with Edge Restraints and Intermediate Stiffeners," Journal of Sound and Vibration, Vol. 123, No. 1, 103-113.
150. Young, P. G., and Dickinson, S. M., 1993, "On the Flexural Vibration of Rectangular-Plates with Straight or Curved Internal Line Supports," Journal of Sound and Vibration, Vol. 162, No. 1, 123-135.
151. Yuan, J., and Dickinson, S. M., 1992, "The Flexural Vibration of Rectangular Plate Systems Approached by Using Artificial Springs in the Rayleigh-Ritz Method," Journal of Sound and Vibration, Vol. 159, No. 1, 39-55.
152. Yuan, J., and Dickinson, S. M., 1994, "The Free-Vibration of Circularly Cylindrical-Shell and Plate Systems," Journal of Sound and Vibration, Vol. 175, No. 2, 241-263
153. Yuan, J., and Dickinson, S. M., 1995, "On the Determination of Phase Constants for the Study of the Free-Vibration of Periodic Structures," Journal of Sound and Vibration, Vol. 179, No. 3, 369-383.
154. Zienkiewicz, O. C., 1977, The Finite Element Method, 3rd Ed., McGraw-Hill, London.