Resonance of a Quasi-Zero Stiffness Vibration System Under Base Excitation with Load Mismatch

Abstract

The primary resonance and 1/3 subharmonic resonance of a quasi-zero stiffness (QZS) vibration system under base excitation with load mismatch are studied in this research. The incremental harmonic balance (IHB) method is applied to obtain highly accurate solutions involving more dynamic behaviors. The effect of the offset displacement mainly caused by overloading on the primary resonance and displacement transmissibility is investigated. The results indicate that the system exhibits a softening characteristic under certain conditions. Although the isolation performance of the QZS system deteriorates, it still outperforms the equivalent linear system for excitation amplitudes that are not too large. The parametric analysis of the 1/3 subharmonic resonance shows that the response is unbounded, and interesting dynamic behaviors can be observed, such as the jump phenomenon. Moreover, the 1/3 subharmonic resonance can be avoided by applying a larger damping or reducing the excitation amplitude to a lower level.

Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

“…Cheng et al [36] found that the nonlinear damping could eliminate the unbounded response of the displacement transmissibility. Cheng et al [37] considered the load mismatch, and found that the QZS isolator still outperformed the equivalent linear isolator. Wang et al [38] connected the upper platform of the isolator with an inerter to enhance the performance.…”

Non-Linear Vibration Isolators with Unknown Excitation and Unmodelled Dynamics: Sliding Mode Active Control

“…This isolator possesses high-static-low-dynamic stiffness so that it can maintain the load-bearing capacity with a small static displacement and achieve a lower natural frequency to enlarge frequency ranges of vibration isolation. But, it should be noted that isolators with QZS are very sensitive facilities and if something occurs to cause deviation of its characteristic parameters (e.g., mismatch of the load and negative stiffness parameters) and/or change in the non-linearity properties of its forces (e.g., destruction of the symmetry), then the isolation performance will change dramatically [19][20][21][22]. This situation is particularly true when the amplitude of excitation is not relatively small, and the isolator is exposed to a sustained excitation.…”