Nonlinear dynamic analysis of piezoelectric functionally graded porous truncated conical panel in thermal environments

In this article, the nonlinear dynamic response and free vibration of functionally graded porous (FGP) truncated conical panel with piezoelectric actuators in thermal environments are investigated by an analytical method. The panel resting on an elastic foundation which is modeled according to the Winkler-Pasternak theory. The material properties including Young's modulus, shear modulus, and density are assumed to smoothly through the shell thickness. Three types of porosity distribution across the thickness, namely, symmetric porosity distribution, non-symmetric porosity, and uniform porosity distribution, are considered. Theoretical formulations are presented based on the first-order shear deformation shell theory with a von Karman-Donnell type of kinematic nonlinearity. The non-linear motion equations and resulting equations are derived by using Hamilton's principle, Galerkin's method, and Runge-Kutta method. Lastly, some numerical results are presented to study the effects of shell characteristics, porosity distribution, porosity coefficient, applied actuator voltage, temperature increment and elastic foundations on the nonlinear dynamic response and the natural frequencies of the piezoelectric FGP truncated conical panel.