Abstract
In this paper, the free vibration of the thick annular sector plate on Pasternak foundation with general boundary conditions is presented by using the three-dimensional elasticity theory and the improved Fourier series method. The displacements of the thick annular sector plate are expanded to be the three-dimensional (3-D) Fourier cosine series supplemented with several auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges with general boundary conditions. This method can be universally applied to any kinds of classical boundaries, elastic boundaries and the combinations of both boundaries without any special change in the solution procedure. The excellent accuracy and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature. Furthermore, numerous new results for thick annular sector plates on Pasternak foundation with general elastic restrains are presented. In addition, comprehensive studies on the effects of the elastic restraint parameters, geometric parameters and elastic foundation coefficients are also reported.
Highlights
Annular sector plates have wide applications in various engineering constructions as one of structure elements, such as aircraft, space vehicles and structures in military industries
Liew and Liu [20] studied the free vibration analysis of moderately thick annular sector plates with classical boundary conditions by the differential quadrature method based on the first-order shear deformation theory
To the best of our knowledge, there is no work reported on the free vibration behavior of thick annular sector plates on Pasternak foundation with general boundary conditions based on the three-dimensional elastic theory
Summary
Annular sector plates have wide applications in various engineering constructions as one of structure elements, such as aircraft, space vehicles and structures in military industries. Shi et al [13] applied the Rayleigh-Ritz method and the improved Fourier series technique to investigate the free vibration of circular, annular and sector thin plate with general boundary conditions. Liew and Liu [20] studied the free vibration analysis of moderately thick annular sector plates with classical boundary conditions by the differential quadrature method based on the first-order shear deformation theory. To the best of our knowledge, there is no work reported on the free vibration behavior of thick annular sector plates on Pasternak foundation with general boundary conditions based on the three-dimensional elastic theory. The authors apply the modified Fourier series technique together with the Rayleigh-Ritz method to provide a new three-dimensional exact solution for the free vibration of thick annular sector plates on the Pasternak foundation with general boundary conditions in this paper. The effects of the boundary conditions, geometric parameters and elastic foundation coefficients on vibration behaviors of the thick annular sector plate are presented
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