WAVE PROPAGATION IN ELASTIC BEAMS USING SPECTRAL FINITE ELEMENT METHOD

Abstract

In this paper, wave propagation in elastic beams is studied using the spectral finite element method. Two beam models considered in the analysis are the Euler-Bernoulli and Timoshenko beam models for transverse motion. The element has an exact dynamic stiffness matrix as it is derived from exact solution to the governing wave equation in frequency domain. The results of fast Fourier transform (FFT) based spectral finite element method (SFEM) considered in this paper is validated by comparing them with the wavelet based spectral finite element method (WSFEM) and/or the conventional finite element method (FEM) results in the published literature. Dispersion relations (plot of wave number and phase speed versus frequency) for the beam are plotted for both the models. First, the natural frequencies of a cantilever beam obtained by the present spectral element method are compared with the analytical and FEM results. Next, wave propagation in a cantilever beam subjected to impact load is considered. Velocity at the free end of the cantilever beam is evaluated by using the Euler-Bernoulli and Timoshenko models. These results are also compared with FEM and WSFEM solutions. Discrepancies between results obtained by using Euler-Bernoulli and Timoshenko models are investigated in detail. The present spectral finite element method provides very accurate solutions when compared with the conventional FEM.