Subharmonic instability and coupled motions in non-linear vibration isolating suspensions

Abstract

The subharmonic behaviour of an undamped non-linear isolating system having springs with cubic, hardening, stress-strain characteristics is studied theoretically and experimentally using an analogue computer. For simplicity the linear natural frequencies of the six normal modes of vibration are so related that dynamic interaction occurs only between pairs of modes one of which is externally excited. Interactions resulting from coupling of any two such modes are studied in detail. The non-linearity of the springs makes subharmonic oscillations possible. It also creates coupling between normal modes yielding a variety of theoretically possible, steady-state coupled subharmonic motions. The coupling of the modes under subharmonic conditions occurs at a frequency where, for the same system, no interaction between the modes would have occurred under harmonic oscillations. The conditions necessary for the existence of coupled oscillations are examined and a stability criterion is established. As a result of instability in coupled subharmonic motions it is found that under certain conditions the non-linear coupling between the two modes can destroy the subharmonic steady-state oscillations of the directly excited mode, yielding an uncoupled harmonic response. Correlation between experimental results and theory gives good qualitative agreement justifying any approximations made during the analysis. First- and second-order subharmonic resonances are examined but harmonic and superharmonic oscillations are excluded.