Dynamic response determination of viscoelastic annular plates using FSDT – perturbation approach

Abstract

In this paper, the transient response of a viscoelastic annular plate which has time-dependent properties is determined mathematically under dynamic transverse load. The axisymmetric conditions are considered in the problem. The viscoelastic properties obey the standard linear solid model in shear and the bulk behavior in elastic. The equations of motion are extracted using Hamilton's principle by small deformation assumption for the elastic condition and they are extended to the viscoelastic form by defining viscoelastic operators based on the separating the bulk and shear behaviors. The displacement field is defined with the first order shear deformation theory by considering the transverse normal strain effect. These equations which contain four coupled partial differential equations with variable coefficients are solved using the perturbation technique. The results are compared with those obtained from the classical plate theory and the finite element method. The presented formulation is useful for parametric study because it does not need to generate mesh and selecting time step for each model; also the running time is short with respect to the finite elements method. For sensitivity analysis, the effects of geometrical and mechanical parameters on the response are investigated by parametric study.