Study on fundamental damped frequency parameters of plates made of FG porous material: a close-form solution

Abstract

In this article, the natural frequencies of viscoelastic annular plates made of functionally graded porous (FGP) materials with assorted boundary conditions are investigated in a closed-form solution for the first time. The porosity variation is a function of the plate thickness according to symmetric and asymmetric distributions. The governing motion equations are derived by considering the first-order shear deformation theory (FSDT), energy method, and the calculus of variations. The viscoelastic properties of the structure are also captured by means of the standard linear solid (SLS) model. The equations of motion, which are a system of partial differential equations with variable coefficients, are then solved using the perturbations methodology. To do so, the equations with variable coefficients are converted to a system with constant coefficients, and the natural frequencies are found analytically in a closed-form solution without any approximation. In addition, a user-defined field (USDFLD) code is developed, which introduces solution-dependent material properties in Abaqus/Standard analyzes, for evaluating the accuracy of the analytical results. Finally, the impact of various parameters including inner-to-outer radius ratios, thickness-to-radius ratios, porosity coefficient, damping exponent, different combinations of boundary conditions, and porosity patterns on the natural frequencies of annular plates are examined.