Out of Plane Free Vibration Analysis of Circular Curved Beam with Variable Cross Section by Spectral Element Method

Abstract

In accordance to the work that was done by the researchers were followed by using various types of computational methods for analysis of curved beams. The work done on the basis of conventional analysis methods and exact methods and that were done by using Quadrature Element Method (QEM), Differential Quadrature Element Method (DQEM), Finite Element Method (FEM), Differential Transformation Element Method (DTEM) etc. And for the consideration of Rotary Inertia and Shear Deformation the Spectral Element Method (SEM) is used in this work.

Spectral Element Method (SEM) is a computational method that was recently developed and used for the out-of-plane free vibration analysis of a circular curved beam with variable Cross Section. For the circular curved beams, the effect on the frequency parameters are studied and the effect by shear deformation and rotary inertia for various boundary conditions are considered. Here initially spectral element matrices are derived for out-of-plane Vibration from the governing differential equations of motion in the local polar co-ordinate system and then after transformed to global cartesian co-ordinates system.

Natural frequencies with consideration of least degrees of freedom will give high accuracy by using SEM. To validate the method some Numerical examples are solved and the results obtained are compared with exact solutions.