Analytical investigation of asymmetric forced vibration behavior of functionally graded porous plates with structural damping

This research presents a first attempt to analytically determine the asymmetric dynamic transverse characteristics of thin to moderately thick viscoelastic functionally graded porous (VFGP) annular plates. Firstly, the material properties of the plate are assumed to have various nonlinear distributions in terms of porosity coefficient. Secondly, the motion equations are obtained through the first-order shear deformation theory (FSDT) of elasticity, the energy method, and the variations calculus. Thirdly, the standard linear solid (SLS) model is adopted to consider the viscoelastic behavior of the plate. Finally, the perturbation procedure together with Fourier series are utilized to solve the system of partial differential equations, and the asymmetrically dynamic response is found in a closed-form solution. To assess the veracity of the analytical findings, an algorithm based on the finite element (FE) method called the user-defined field (USDFLD) code is developed. In order to benchmark the present study, the dynamic response of VFGP annular plates is scrutinized under two types of excitations (impulsive and step), four different types of radial load profiles (such as constant, linear, parabolic, and sine distributions), and various asymmetric circumferential loads. Moreover, the influence of various geometrical and material characteristics on the dynamic response of VFGP annular plates is investigated.