Original scientific paper
https://doi.org/10.31534/engmod.2018.1-2.ri.01_vjan
Spectral element analysis of free - vibration of Timoshenko beam
Saida Hamioud
; Department of Civil Engineering, University of Jijel, Jijel, ALGERIA
Salah Khalfallah
; Department of Mechanical Engineering, Polytechnic National School, Constantine, ALGERIA
Abstract
The paper describes free vibration of Timoshenko beam by using spectral element method. Based on the partial differential equation of motion, the dynamic stiffness matrix in the frequency domain is formulated. In this case, natural frequencies for simply supported beam are obtained for each mode of vibration. In this study, three solutions are presented: (1) the analytical solution, (2) the finite element method, and (3) the spectral element method. In the last method, the beam is described by one element only, but in finite element modelling, the number of elements varies in order to improve the quality of the solution. Numerical results obtained by these three methods are collected. The spectral element method displays high performance compared to the finite element approach, and is considered as interesting tool in the structural dynamic field.
Keywords
analytical solution; Euler-Bernoulli beam; finite element method; free vibration; spectral element method; spectral stiffness matrix; Timoshenko beam
Hrčak ID:
206317
URI
Publication date:
7.9.2018.
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