Axial-Flexural-Shear Coupled Vibration Analysis of Timoshenko Composite Beam Using Spectral Element Method

Abstract

The free vibration analysis of an axial-?exural-shear coupled composite beam with di?erent boundary conditions has been studied by many researchers using various computational methods of analysis such as Finite Element Method(FEM),Di?erential Transformation Element Method(DTEM),Quadrature Element Method(QEM),Di?erential Quadrature Element Method(DQEM) etc.,besides the traditional mathematical methods and exact methods.In this study the Spectral Element Method(SEM)for analysis of free vibration of both symmetrical as well as asymmetrical composite beam with various boundary conditions is presented considering the e?ects of axial,bending and shear deformations.Initially,spectral element matrices in the time domain are derived for axial-bending-shear coupled vibration from the governing di?erential equations of motion by using Hamilton principle and after that, it has been transformed into the frequency domain.With the consideration of least number of elements the higher accuracy in the natural frequencies is possible using SEM, thus proving that this method is highly accurate and having very high computational e?ciency.So to con?rm the validity of this method several numerical examples are presented and the results are then compared with the other existing solutions.