Nonlinear large amplitude vibrations of annular sector functionally graded porous composite plates under instantaneous hygro-thermal shock

Abstract

In this paper, the nonlinear large amplitude vibrations of functionally graded material porous annular sector plates have been investigated. The effects of considering nonlinearity in scrutinizing the large amplitude thermally induced vibrations of the annular sector plates have been studied. Additionally, in this work, the effects of moisture distribution and the presence of material porosity are taken into account. Material and temperature distribution in the thickness direction of the plate cause changes in the hygro-thermo-mechanical material properties in the corresponding direction. To define the dependence of material properties on position and temperature, the power law distribution and the Touloukian formula are employed, respectively. Next, according to the classical theory of thermoelasticity, the one-dimensional heat conduction equation along the thickness direction of the plate is solved and the temperature profile is obtained. Afterward, knowing the temperature distribution, the nonlinear equations of motion, which are derived employing Hamilton’s principle, are solved for each time step. To numerically solve the equations, first, using the generalized differential quadrature method (GDQM), the spatial derivatives are discretized and a differential equation with only the time derivatives is achieved, then the time-dependent differential equation is solved utilizing the Newmark implicit time integration method. Finally, a parametric numerical analysis is conducted to investigate the effects of various parameters on the vibrational behavior of the plate.