Dynamic analysis of beam resting on a nonlinear viscoelastic foundation subjected to two concentrated moving loads

Abstract

The paper studies a dynamic response of a Timoshenko beam resting on a third order nonlinear viscoelastic foundation. A single beam modeled as theory Timoshenko with a constant cross-section. The concentrated moving load is considered with two concentrated moving loads. The foundation is taken as a third order nonlinear viscoelastic foundation with six parameters. Therefore responses of third order nolinear deflection, the effects at the same time of the shear deformable beams and the shear deformation of foundations are considered. The Galerkin method and considering integral quadrature method are utilized transforming differential governing equations of motion into the ordinary differential equations. The numercial integration method is used to solve differential equations and root of equations which is deflection of beam are determined. The numercial results show that dependence of the convergence rate of the Galerkin truncation and the vertical deflection of the beam on system parameters.