High frequency shaking induced by low frequency forcing: Periodic oscillations in a spring–cable system

We investigate the response of a piecewise linear spring to very low frequency forcing. It has been observed that the bifurcation picture is very complicated with many multiple periodic responses with a high frequency component. We show many new aspects of this phenomenon, including what happens if the nonlinearity is smoothed out. Methods used include Newton’s method, in combination with continuation algorithms, and a steepest descent method for finding new isolated branches of solutions.