Nonstationary Vibration of a System with Backlash Passing through a Resonance

Abstract

When a system with backlash is subjected to an exciting force, of which the frequency linearly increases or decreases with time and passes through a resonance, nonstationary responses of the system are numerically analyzed and formulas for estimating the maximum amplitudes of the responses are proposed. The evaluation errors are below 25% over the range considered here comparing to the numerically integrated results. The above formulas are derived from a comparison of the two maximum amplitudes, one of which is obtained from a response curve calculated by integrating the equations of motion of the backlash system and the other from the estimation equations of the maximum amplitude for a linear systems passing through a resonance.