In-Plane Free Vibration Analysis of Circular Curved Beam with Varying Cross-Section by Spectral Element Method

Abstract

Spectral Element Method, a computational method recently developed is used for the in-plane free vibration analysis of circular curved beams with varying cross-section. The effects on the frequency parameters of circular curved beams with varying cross-section are studied taking into consideration the effects due to shear deformation and rotatory inertia for various conventional boundary conditions. For this initially, spectral element matrices are derived for in-plane vibration from the governing differential equations of motion in the local polar co-ordinate system and there after transformed to the global cartesian co-ordinate system.

Frequency parameters are obtained for circular curved beams with varying cross-section by employing the spectral element method. To validate this method some numerical examples are also solved and the results obtained are compared with existing literatures.