Buckling and vibration of polar orthotropic circular plate resting on Winkler foundation

A.W. Leissa, Vibration of plates, NASA, SP-160, 1969. Leissa, 1987, Recent studies in plate vibrations 1981–1985, part-II: complicating effects, The Shock and Vibration Digest, 19, 10, 10.1177/058310248701900304 Ramaiah, 1973, Natural frequencies of polar orthotropic annular plates, Journal of Sound and Vibration, 26, 517, 10.1016/S0022-460X(73)80217-2 Dyka, 1979, Vibration and stability of spinning polar orthotropic annular plates reinforced with edge beams, Journal of Sound and Vibration, 64, 223, 10.1016/0022-460X(79)90647-3 Gunaratnam, 1989, Transverse vibration and stability of polar orthotropic circular plates: high level relationship, Journal of Sound and Vibration, 137, 383, 10.1016/0022-460X(89)90632-9 Kim, 1990, The flexural vibration of thin isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries, Journal of Sound and Vibration, 143, 171, 10.1016/0022-460X(90)90576-L Bhushan, 1993, Buckling of tapered orthotropic circular plates using a computationally economic approach, Computers & Structures, 46, 421, 10.1016/0045-7949(93)90212-V Liu, 1995, A simple finite element analysis of axisymmetric vibration of annular and circular plates, International Journal of Mechanical Sciences, 37, 861, 10.1016/0020-7403(94)00099-6 Bhushan, 1996, Asymmetric buckling of layered orthotropic circular and annular plates of varying thickness using a computationally economic semi analytic finite element approach, Computers & Structures, 59, 21, 10.1016/0045-7949(95)00241-3 Gupta, 1998, Free vibration of polar orthotropic circular plates of variable thickness with elastically restrained edge, Journal of Sound and Vibration, 213, 429, 10.1006/jsvi.1997.1463 Gupta, 1998, Asymmetric vibration and elastic stability of polar orthotropic circular plate of linearly varying profile, Journal of Sound and Vibration, 215, 123, 10.1006/jsvi.1998.1589 Szilard, 1974 Chonan, 1980, Random vibration of an initially stressed thick plate on an elastic foundation, Journal of Sound and Vibration, 71, 117, 10.1016/0022-460X(80)90412-5 Gupta, 1990, Effect of elastic foundation on axisymmetric vibration of polar orthotropic circular plates of variable thickness, Journal of Sound and Vibration, 139, 503, 10.1016/0022-460X(90)90679-T Liew, 1996, Differential quadrature method for Mindlin plates on Winkler foundation, International Journal of Mechanical Sciences, 38, 405, 10.1016/0020-7403(95)00062-3 Wang, 1977, Natural frequencies of Timoshenko beams on pasternak foundation, Journal of Sound and Vibration, 51, 149, 10.1016/S0022-460X(77)80029-1 Bhattacharya, 1977, Free vibration of plates on Vlasov's foundation, Journal of Sound and Vibration, 54, 464, 10.1016/0022-460X(77)90459-X Gupta, 1986, Buckling and vibration of polar orthotropic annular plates on an elastic foundation subjected to hydrostatic peripheral loading, Journal of Sound and Vibration, 109, 423, 10.1016/S0022-460X(86)80379-0 Greenberg, 1979, Flexural vibrations of certain full and annular composite orthotropic plates, Journal of the Acoustical Society of America, 66, 501, 10.1121/1.383104 Chen, 1998, Finite element analysis of the lateral vibration of thin annular and circular plates with variable thickness, ASME Journal of Vibration and Acoustics, 120, 747, 10.1115/1.2893893 Liu, 2000, Finite element analysis of three dimensional vibrations of thick circular and annular plates, Journal of Sound and Vibration, 233, 63, 10.1006/jsvi.1999.2791 Charbonneau, 2001, Semi-analytical shape functions in the finite element analysis of rectangular plates, Journal of Sound and Vibration, 242, 427, 10.1006/jsvi.2000.3373 Ritz, 1909, Uber eine neue methode zur losung geuisser variations probleme der mathematischen physik, Journal fur Reine und Angewandte Mathematic, 135, 1, 10.1515/crll.1909.135.1 Liew, 1995, Research on thick plate vibration: a literature survey, Journal of Sound and Vibration, 180, 163, 10.1006/jsvi.1995.0072 Bhat, 1985, Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh–Ritz method, Journal of Sound and Vibration, 102, 493, 10.1016/S0022-460X(85)80109-7 Bhat, 1987, Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables, Journal of Sound and Vibration, 114, 65, 10.1016/S0022-460X(87)80234-1 Dickinson, 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, 108, 51, 10.1016/S0022-460X(86)80310-8 Liew, 1989, Study on flexural vibration of triangular composite plates influenced by fibre orientation, Composite Structures, 13, 123, 10.1016/0263-8223(89)90050-0 Liew, 1990, Free vibration analysis of rectangular plates influenced by fiber orientation, Computers & Structures, 34, 79, 10.1016/0045-7949(90)90302-I Liew, 1990, Application of two-dimensional orthogonal plate function to flexural vibration of skew plates, Journal of Sound and Vibration, 139, 241, 10.1016/0022-460X(90)90885-4 Liew, 1994, Vibration of clamped circular symmetric laminates, Journal of Vibration and Acoustics, 116, 141, 10.1115/1.2930404 Zhou, 2002, Three dimensional vibration analysis of thick rectangular plates using Chebyshev polynomials and Ritz method, International Journal of Solids and Structures, 39, 6339, 10.1016/S0020-7683(02)00460-2 Zhou, 2003, Three dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method, International Journal of Solids and Structures, 40, 3089, 10.1016/S0020-7683(03)00114-8 Kang, 2003, Three dimensional vibration analysis of thick circular and annular plates with non-linear thickness variation, Computers & Structures, 81, 1663, 10.1016/S0045-7949(03)00168-8 Kang, 2005, Approximate closed form solutions for free vibration of polar orthotropic circular plates, Applied Acoustics, 66, 1162, 10.1016/j.apacoust.2004.09.009 Lekhnitskii, 1985 Laura, 1991, Free vibration of a solid circular plate of linearly varying thickness and attached to a Winkler type foundation, Journal of Sound and Vibration, 144, 149, 10.1016/0022-460X(91)90738-6 Pardoen, 1978, Asymmetric vibration and stability of circular plates, Computers & Structures, 9, 89, 10.1016/0045-7949(78)90062-7 A.S. Volmir, Stability of elastic system, FTD-Mt-64-335, Wp-AFB, Ohio, 1966. Gutierrez, 1996, Vibration and elastic stability of thin circular plates with variable profile, Journal of Sound and Vibration, 195, 391, 10.1006/jsvi.1996.0433