Nonlinear free vibration of FGM sandwich plates with porosity under uniaxial compressive loads in thermal environments

This paper aims to examine the influences of porosity, initial uniaxial compressive loads and thermal environments on the nonlinear free vibration of functionally graded material (FGM) sandwich plates. The properties of constitutive materials are considered to be temperature dependent and effective properties of porous FGM are estimated using a modified rule of mixture. The pores are dispersed in FGM according to even and uneven distribution types. Governing equations in terms of deflection and stress function are established based on first order shear deformation theory including geometric imperfection and von Kármán nonlinearity. These equations are solved by means of analytical solutions and Galerkin method to derive a nonlinear ordinary differential equation. This differential equation is numerically solved employing the fourth–order Runge–Kutta scheme to determine the frequencies of nonlinear free vibration of sandwich plates. A parametric study is carried out to examine various effects of uniaxial loads, pore volume fraction and distribution, imperfection, thermal environments and in-plane constraints of unloaded edges on the natural frequencies and frequency–amplitude curves. It is found that initial compressive loads decrease natural frequencies and strengthen the frequency nonlinearity of the sandwich plates. Additionally, the frequency nonlinearity is more significant when the unloaded edges are restrained more rigorously and temperature is more elevated. The results also detect that geometric imperfection increases and decreases the frequency ratios in the smaller and larger regions of maximum amplitude of deflection, respectively.