The natural frequencies of waves in helical springs

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.