Linear dynamics of elastic helical springs: asymptotic analysis of wave propagation

Abstract

Helical springs serve as vibration isolators in virtually any suspension system. A variety of theories to describe the dynamic behaviour of these structural elements, which involves interaction of flexural, torsion and longitudinal waves, can be found in the literature. Alongside this, various approximate methods are employed to determine the eigenfrequencies of vibrations of springs. In this paper, the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves. This paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed. It allows for the identification of significant regimes of linear wave motion in a helical spring. In each of these regimes, simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution. Mode shapes associated with each wavenumber are also analysed.