Optimization of secondary suspension of piecewise linear vibration isolation systems

Abstract

A comprehensive optimal design solution is presented for piecewise-linear vibration isolation systems. First, primary suspension optimum parameters are established, followed by an investigation of jump-avoidance conditions for the secondary suspension. Within the no-jump zones, an optimal design solution is then obtained for the secondary system and overall results are discussed. Averaging method is employed to obtain an implicit function for frequency response of a bilinear system under steady-state conditions. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of ‘jump’ does not occur and the system response is functional and unique. Optimal stiffness and damping parameters for the primary suspension are extracted from a recently established work for passive linear vibration systems. For each point of the primary suspension optimal curve, jump-free zones are identified. Iterating this process, a boundary surface between no-jump (unique response) and jump (multiple-response) areas is established. Keeping optimal parameters for the primary suspension system fixed, the secondary suspension stiffness and damping parameters are varied inside the no-jump zones to explore optimum solutions for the secondary. The root mean square (RMS) of the absolute acceleration is minimized against the RMS of the relative displacement ( η). It is observed that there is a certain band of parameters defined by primary damping, within which a valid frequency response can be obtained. An optimum numerical solution is sought within this band of parameters. Optimal solution curves are achieved for the secondary suspension. These can be used in conjunction with the optimal curve for the primary suspension to select design parameter values for the best possible vibration isolation performance in a given application.