The natural frequencies of waves in helical springs

Anis Hamza; Sami Ayadi; Ezzeddine Hadj-Taïeb

doi:10.1016/j.crme.2013.09.006

The natural frequencies of waves in helical springs

Anis Hamza ¹ ; Sami Ayadi ¹; Ezzeddine Hadj-Taïeb ¹

¹ Laboratory of Applied Fluid Mechanics and Modelling, University of Sfax, National Engineering School of Sfax (ENIS), BP 1173, 3038 Sfax, Tunisia

Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 672-686.

Abstract

In this study, the vibrations of a coil, excited axially, in helical compression springs such as tamping rammers are discussed. The mathematical formulation is comprised of a system of four partial differential equations of first-order hyperbolic type, as the unknown variables are angular and axial deformations and velocities. The numerical resolution is performed by the conservative finite difference scheme of Lax–Wendroff. The impedance method is applied to calculate the frequency spectrum. The results obtained with this method were used to analyze the evolution in time of deformations and velocities in different sections of the spring resulting from a sinusoidal excitation of the axial velocity applied at the end of the spring. These results clearly show the effect of the interaction between the slow axial waves and the fast angular waves, the resonance and other phenomena related to wave propagations such as wave reflections and beat.

Received: 2013-01-15
Accepted: 2013-09-28
Published online: 2013-09-01

DOI: 10.1016/j.crme.2013.09.006

Mots-clés : Helical compression springs, Impedance method, Method of Lax–Wendroff, Resonance and beat phenomenon, Poisson coupling

Author's affiliations:

Anis Hamza ¹; Sami Ayadi ¹; Ezzeddine Hadj-Taïeb ¹

¹ Laboratory of Applied Fluid Mechanics and Modelling, University of Sfax, National Engineering School of Sfax (ENIS), BP 1173, 3038 Sfax, Tunisia

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     title = {The natural frequencies of waves in helical springs},
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     language = {en},
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Anis Hamza; Sami Ayadi; Ezzeddine Hadj-Taïeb. The natural frequencies of waves in helical springs. Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 672-686. doi : 10.1016/j.crme.2013.09.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.09.006/

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