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Resonance phenomenon of strain waves in helical compression springs

Published online by Cambridge University Press:  30 September 2013

Anis Hamza ,
Sami Ayadi  and
Ezzeddine Hadj-Taïeb
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Abstract

In this study, vibration of helical compression springs, excited axially, is discussed. The mathematical formulation of the dynamic behavior of the springs is composed of a system of four partial differential equations of first order hyperbolic type, which are the equations of momentum and the laws of constitution. The principle unknown variables are angular and axial deformations and velocities. In small deformations, the coefficients of the equation system are constant and the model describes the linear dynamic behavior of coil springs. The impedance method is applied to calculate the frequency spectrum and to study the natural frequency response. The study takes into account the dynamic coupling between the axial and angular waves due to the effects of Poisson’s ratio. The results show two fundamental frequencies corresponding to the two wave speeds: fast angular waves and slow axial waves. The numerical resolution is performed by the conservative finite difference scheme of Lax-Wendroff and the finite element method. The results were used to analyze the evolution in time of deformations and velocities in different sections of the spring due to a sinusoidal excitation of the axial velocity applied at the end of the spring and to show the effect of the interaction between the axial and angular waves. These results clearly show the resonance and other phenomena related to wave propagations such as wave reflections and beat.

Keywords

Helical compression springimpedance methodmethod of Lax-Wendrofffinite element methodresonance and beat phenomenaPoisson couplingRessort hélicoïdal de compressionméthode d’impédanceméthode de Lax-Wendroffméthode des éléments finisphénomènes de résonance et battementcouplage de Poisson
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 4 , 2013 , pp. 253 - 265
Copyright
© AFM, EDP Sciences 2013

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