Differential Quadrature Method for Vibration Analysis of Finite Beams on Nonlinear Viscoelastic Foundations

Abstract

This paper investigates finite beams resting on nonlinear viscoelastic foundations. Nonlinear foundation is assumed to be cubic. It studies free vibration and dynamic response of the beam subjected to a harmonic moving load. The differential quadrature (DQ) methods are applied directly to the governing equations. Based on the numerical solutions, the natural frequencies are obtained with discrete Fourier transform (DFT). The frequencies of nonlinear vibration are compared with the complex modal analysis method for the corresponding governing equations without nonlinear parts. The effects of system parameters on natural frequencies and dynamic response are numerically studied