Response of Timoshenko beam on nonlinear viscoelastic foundation subjected to a moving load
Abstract
The paper studies the dynamic response of a Timoshenko beam resting on a third order nonlinear viscoelastic foundation subjected to a moving load. Basing on the theory Timoshenko, a single beam with a constant cross-section is described. The foundation modal is taken as the third order nonlinear viscoelastic foundation with six independent parameters. Therefore, responses of the third order nonlinear deflection, the effects at the same time of the shear deformable beams and the shear deformation of foundation are considered. The Galerkin method and considering integral quadrature method are utilized to transform differential governing equations of motion into the ordinary differential equations. The numerical integration Newmark method is used to solve differential equations and root of equations which is deflection of beam is determined. The numerical results show the dependence of the convergence rate of the Galerkin truncation and the vertical deflection of the beam on system parameters.