Free Flexural Vibration of Multiple Stepped Beams by Spectral Element Method

Abstract

The free vibration analyses of multiple-stepped Bernoulli-Euler beam with various boundary conditions have been studied by many researchers using different methods of analysis such as Differential Quadrature Element Method (DQEM), Composite Element Method (CEM), Admonian Decomposition Method (ADM), Differential Quadrature Method (DQM), Local adaptive Differential Quadrature Method (LaDQM), Discrete Singular Convolution (DSC) algorithm etc., besides the conventional analytical methods and finite element methods. In this work the Spectral Element Method (SEM) for analysis of stepped-beams has been used. The second part of the work is concerned with the free flexural vibration of multiple-stepped Timoshenko beam with various boundary conditions using the Spectral Element Method (SEM). Accurate computation of even the higher modes of vibration frequencies with consideration of least number of degrees of freedom is possible using SEM thus promising very high computational efficiency. Validation of this method is performed with various numerical solutions. A comparison between application of both Euler-Bernoulli and Timoshenko beam theory to the same beam is carried out and various important physical parameters are also investigated