Nonlinear free and forced vibration analysis of thin circular functionally graded plates

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Karman's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates

Natural frequencies of heated annular and circular plates

This study aimed to investigate axisymmetric post-buckling behavior of a circular plate made of porous material under uniformly distributed radial compression with simply supported and clamped boundary conditions. Pores are saturated with fluid and plate properties vary continuously in the thickness direction. Governing equations are obtained based on classical plate theory and applying Sanders nonlinear strain-displacement relation. Shooting numerical method is used to solve the governing equations of problem. Effects of porosity coefficient, pore distribution, pore fluid compressibility, thickness change and boundary conditions on the post-buckling behavior of the plate are investigated. The results obtained for post-bucking of homogeneous/isotropic plates and critical buckling load of porous plates are compared with the results of other researchers.

S.-R Li

Papers

Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass