On the asymmetric dynamic response of viscoelastic sector plate made of FG polymer foam

Abstract

This work provides an analytical investigation of the damped forced vibration behavior of viscoelastic annular sector plates made of porous polymer foam. For this aim, the motion equations are obtained through first-order shear deformation theory (FSDT) in conjunction with the energy method and the calculus of variations. Three distinct types of pore distribution are explored in the plate thickness such as porosity symmetric distribution type 1 (PSDT1), porosity symmetric distribution type 2 (PSDT2), and porosity non-symmetric distribution (PND). Then, the obtained relations are extended to constitutive equations by considering the standard linear solid (SLS) viscoelastic model. The perturbation technique and Fourier series are employed to solve the system of equations with variable coefficients. The equations with variable coefficients are changed to a system with constant coefficients by inserting a new variable, and the asymmetrically dynamic response is computed analytically in a closed-form solution. Then, the transient dynamic behavior of viscoelastic functionally graded porous (VFGP) annular sector plates is detailed for various types of radial and asymmetric circumferential loadings. Furthermore, a user-defined field (USDFLD) code is developed for evaluating the reliability of the analytical findings using finite element (FE) software. Finally, we have benchmarked the effectiveness of our framework by investigating several geometrical parameters, material properties, and loadings types.