Theoretical Analysis for Force Transmissibility and Jump Phenomena of Duffing Spring Type Vibration Isolator

Abstract

In order to study the common nonlinear characteristics of the vibration isolator, a single degree of freedom system with cubic restoring force is introduced to describe the nonlinear vibration isolation system in the paper and the harmonic balance method was applied to investigate the primary resonance near the natural frequency of the system. Based on Routh–Hurwitz stability criterion, it was clarified theoretically that the region surrounded by the curve of the vertical tangential points in the curve cluster of the primary resonance amplitude frequency characteristics was instable. In addition, the equations of the jump frequency and force transmissibility were derived. The calculated results showed that the jump, hysteresis, stable and instable phenomena would take place for the force transmissibility of the isolator system and the effect of high frequency components of the transmitting force was limited; the damping, coefficient of nonlinear restoring force and the excitation amplitude had an influence on the force transmissibility whose frequencies were in the region of the resonance frequencies but not on those whose frequencies were lower than the resonance frequencies, and only the damping would affect the force transmissibility whose frequencies were higher than the resonance frequencies. Finally, the equation of the start frequency, on the condition that the force transmissibility was less than 1, was presented.