Stability Analysis of a Piecewise Nonlinear Vibration Isolator

Abstract

Many vibration isolators can be modeled with a discontinuity in the stiffness and damping coefficients. The sudden change in the values of the coefficients can be represented as a piecewise linear or nonlinear function. Soft suspensions are best for isolation; however, a nonlinear hardening suspension is required to minimize relative displacement at high amplitudes. Often, the physical design limits the relative displacement. Taking advantage of nonlinearity in the suspension is not enough in limiting the relative displacement at very high amplitude. Therefore, a secondary suspension must be involved to limit very high relative displacements. In this investigation, the averaging method was applied to the differential equation generated from the model to find the frequency response. A sensitivity analysis was performed to find regions of instability in the frequency response