Dynamic analysis of nonlinear elasticity beam using DQ semi-analytical method

This paper presents a new semi-analytical approach for the nonlinear vibration analysis of nonlinear elasticity beam. The time domain response and frequency response of a nonlinear elasticity beam´s free vibration will be obtained, Considering the efforts of the static deformation on the dynamic characteristics. The method makes use of Linz Ted-Poincare perturbation technique to transform the nonlinear governing equations into a linear differential equation system, whose solutions are then sought through the use of differential quadrature approximation in space domain and an analytical series expansion in time domain. Validation of present method is conducted in numerical examples through direct comparisons with existing solution, showing that the proposed semi-analytical method has excellent convergence and can give very accurate results at a long time interval. This method successfully avoids the accumulation of errors and has good precision, which makes it possible to the solution of the nonlinear dynamic problems.