Higher-order accurate compact difference solutions for vibration problems of one dimensional continuous systems

Authors

  • Mondher Yahiaoui Ecole de l’Aviation de Borj El Amri Borj El Amri 142, Tunisia

DOI:

https://doi.org/10.13052/EJCM.19.771-794

Keywords:

fourth-order and seventh-order accuracy, compact differences, boundary-value problems, eigenvalues, vibrations of continuous systems, tapered beams, shear deformation, rotary inertia

Abstract

In this paper, we present a fourth-order accurate and a seventh-order accurate, one-step compact difference methods. These methods can be used to solve initial or boundaryvalue problems which can be modeled by a first-order linear system of differential equations. It is then shown in detail how these methods can be used to solve vibration problems of onedimensional continuous systems. Natural frequencies of a cantilever beam in transverse vibrations are computed and the results are compared to analytical ones to prove the high accuracy and efficiency of both methods. A comparison was also made to a finite element solution and the results have shown that both compact-difference methods yield more accurate values even with a reduced number of intervals.

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Published

2011-11-20

How to Cite

Yahiaoui, M. . (2011). Higher-order accurate compact difference solutions for vibration problems of one dimensional continuous systems. European Journal of Computational Mechanics, 19(8), 771–794. https://doi.org/10.13052/EJCM.19.771-794

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Original Article