Propagation of strain waves in cylindrical helical springs

Abstract

This paper discusses the vibrations of a coil, which is excited axially, in helical compression springs. The mathematical formula is composed of a system of four hyperbolic partial differential equations of first order with unknown variables, which are angular and axial deformations and velocities. The numerical resolution is based on the conservative finite difference scheme of Lax-Wendroff. The impedance method is applied to calculate the frequency spectrum. The spring is excited by a sinusoidal axial velocity at its end. The results obtained by using this method are used to analyze the evolution in time of deformations and velocities in different sections. These results clearly show the effect of the interaction between the slow axial waves and the fast angular waves. Indeed, the amplification was more important for the axial strain than for the rotational one that was caused by the effect of coupling Poisson. In addition to this, the resonance phenomenon and other phenomena related to wave propagations such as wave reflections and beat are analyzed.