Free Vibration Analysis of Circular Curved Beam by Spectral Element Method

Abstract

The free vibration analysis of a curved beam with various boundary conditions has been studied by many researchers using different computational methods of analysis such as Quadrature Element Method (QEM), Differential Quadrature Element Method (DQEM), Finite Element Method (FEM), Differential Transformation Element Method (DTEM) etc., besides the conventional analytical methods and exact methods. In this work the Spectral Element Method (SEM) for both out-of-plane (transverse) and in-plane free vibration of a curved beam with various boundary conditions is presented considering the effects of rotary inertia and shear deformation. Initially, spectral element matrices are derived for both out-of-plane and in-plane vibration from the governing differential equations of motion in the local polar coordinate system and thereafter transformed to the global Cartesian coordinate system. Higher accuracy of the natural frequencies with consideration of least degrees of freedom is possible using SEM, thus proving the method to be of very high computational efficiency. To confirm the validity of this method some numerical examples are presented and the results are compared with the other existing solutions.