Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment

Abstract

The nonlinear eigenfrequency responses of a functionally graded material (FGM) panel in a thermal environment are numerically estimated in the present article using the finite element method (FEM). The constituents of the FGM are considered as the function of the temperature. For the evaluation of material properties of the FGM panel, Voigt’s micromechanical model is used in conjunction with three distinct types of material distribution patterns, namely power-law (PL), sigmoid (SM), and exponential (EN). Also, two kinds of porosity distributions, i.e. even (PT-I) and uneven (PT-II) through the panel thickness are considered in the present work. HSDT kinematics and Green–Lagrange nonlinear strain terms are employed to prepare a mathematical model of the FG panel. The governing equation is obtained using Hamilton’s principle, and a direct iterative technique is used to compute the final vibration responses. The convergence and validation are performed to check the stability and accuracy of the proposed model. Afterwards, several numerical examples are solved to demonstrate the proposed model efficacy in terms of currently adopted input parameters on the frequency (nonlinear) responses deliberated in detail.