Technical Journal, Vol. 10 No. 3-4, 2016.
Preliminary communication
Free-vibration of Bernoulli-Euler beam using the spectral element method
Saida Hamioud
; National Polytechnic School of Constantine, Constantine, Algeria
Salah Khalfallah
; University of Jijel, Civil Engineering Departement, Jijel, Algeria
Abstract
The present work describes the spectral finite element formulation and the solution of Bernoulli-Euler free vibrations beams. The formulation including the partial differential equations of motion, the spectral displacement field and the dynamic stiffness matrix, is established in the scope of the spectral element method. The development is recognized for the general case without considering boundary conditions. The work describes the solution of the problem using three distinct methods: (1) the finite element method, (2) the analytical method and (3) the spectral element method. Particularly, natural frequencies for clamped-free vibration of Bernoulli-Euler beams are established. In the finite element approach, the element number varied in order to improve the accurate solution. Contrary, the spectral element method requires only one to two elements. Results using this method are compared with the finite element method and analytical procedure ones. The spectral element method shows notable advantages compared to the finite element method reducing the number of elements as well as increasing the accuracy.
Keywords
Analytical solution; Bernoulli- Euler beam; finite element method; free vibration; Spectral element method; spectral stiffness matrix
Hrčak ID:
171830
URI
Publication date:
15.12.2016.
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