Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections

One degree of freedom quasi-zero stiffness mechanical oscillators are characterised by having a spring with a very low stiffness at some point in the force-deflection curve, and their investigation has been mainly motivated for vibration isolation and control purposes. Unlike conventional quasi-zero stiffness mechanical oscillators, which exhibit a very low dynamic stiffness for small deflections, this paper presents a complementary case, not yet systematically addressed in the literature, where the low dynamic stiffness is achieved at large deflections. As a consequence, the equivalent spring exhibits a softening rather than a hardening behaviour, and a lower limit for the resonance frequency which bends to the lower frequencies may be derived. The oscillator is physically realised by using four springs properly arranged, rather than two, as classically reported in the literature. An approximate analytic insight is presented, as this allows the derivation of simple easy-to-use relationships to help the design strategy.