Sensitivity analysis of frequency response of a piecewise linear system in frequency island

In this paper, we analyze the frequency response of a piecewise linear suspension system. Dynamical characteristics of the suspension will suddenly change when its relative displacement exceeds a clearance. Piecewise linear characteristics occur, for example, wherever we use stoppers to prevent the system from excessive relative displacement. A modified averaging method is used to find the frequency response of the system to a harmonic base excitation. A frequency island is observed, which corresponds to large amplitude vibration for a certain range of system parameters. The island is an isolated region that cannot be reached by the variation of excitation frequency and depends upon initial conditions. On the frequency island, the isolator amplifies the amplitude of vibration rather than suppressing it. This will be dangerous in applications where stoppers are installed to ensure relative displacement is limited. The ranges of system parameters causing the frequency island are determined. The results obtained by an analytical method are verified using numerical simulation.