Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading

Abstract

In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one.

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

“…Kamrafard et al. 23 used Hamilton principle for the vibration and buckling analysis of annular porous plate. Bennoun et al.…”

“…The vibration characteristic of super elliptical plate was investigated by Hasrati et al 21 Zhong et al 22 employed the triangular DQM for analyzing the flexural response of the elliptical Reissner-Mindlin plate supported by Pasternak foundation. Kamrafard et al 23 used Hamilton principle for the vibration and buckling analysis of annular porous plate. Bennoun et al 24 by employing a five-variable refined plate theory analyzed the vibration behavior of the sandwich FGP.…”

Electromechanical Vibration Characteristics of Porous Bimorph and Unimorph Doubly Curved Panels

“…Recently, Rezaei et al [35][36][37][38][39] proposed some analytical methods to study the static and dynamical behaviors of porous plates according to different mechanical displacement models. Kamranfard et al [40] developed an exact solution to investigate the free vibration and buckling behavior of annular porous plates within the Hamilton's principle and FSDT. Wang and co-authors [41,42] conducted research studies on the nonlinear vibration of FGM rectangular plates with porosities moving in a thermal environment and contacting with liquid.…”

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

“…Kamranfard et al. 19 and Thang et al. 20 investigated the elastic buckling and free vibration analyses of annular sectorial porous plates and porous-cellular plates.…”