Damped response of porous functionally graded viscoelastic cylindrical shells

Abstract

In this article, the behavior of viscoelastic porous functionally graded (FG) shells regarding the free and damped forced vibration analysis is investigated. The differential equations are derived by using higher order shear deformation theory. Using Hamilton’s principle and the energy method, the equations of motion are obtained and solved using Navier’s method. The damping effect is implemented into the analysis by means of Kelvin and linear standard viscoelastic models. With the correspondence principle, the transition from elastic material properties to viscoelastic material properties is achieved. First, a free vibration analysis is performed to verify the accuracy of the developed algorithm and obtained results are compared with the existing studies in the literature. Afterwards, a parametric study considering two different viscoelasticity models is performed. In the first parametric example, damped forced vibration analysis is performed for simply supported FG cylindrical shell using linear standard viscoelastic model as the viscoelastic model. Then, damped forced analysis is performed using Kelvin viscoelastic model for simply supported FG cylindrical shell. Analyses are performed in Laplace domain. The obtained results are transferred to time domain using Durbin’s inverse Laplace transform method. The displacement graphs are given for the damped forced vibration examples. In the performed parametric studies, the effects of various porosity coefficients, ratios of instantaneous value, retardation times of the relaxation function and damping ratios on the analysis are investigated.