Analysis and design of nonlinear damping and its applications

Abstract

Understanding the damping mechanism in dynamic systems is important for their utilisation and analysis. Dangerous situations could occur without or with relatively low damping, especially under resonance. There are two main methods used for vibration control: active and passive. Compared to active control methods, passive vibration control methods are more reliable, consume less energy, and are effective with optimal vibration protection devices. Passive vibration control can be achieved by employing damping mechanisms, in the form of vibration isolators or tuned-mass dampers. This study analysed a bio-inspired nonlinear damping mechanism, and two applications of this nonlinear damping are developed: a nonlinear tuned-mass damper (X-absorber) and a nonlinear vibration isolator (X-mount). In a linear damping system, enhanced damping suppresses the vibration amplitude near the resonance point, while causing performance deterioration at higher excitation frequencies. Therefore, the design and analysis of nonlinear damping for vibration isolators are necessary and important. Recently, a bio-inspired limb-like structure (LLS) or X-shaped structure was developed and used in numerous applications owing to its beneficial nonlinearities and tuneable properties. By utilising this bio-inspired structure, geometrically nonlinear damping can be achieved, which could improve the performance of the isolator not only at resonance, but also at higher frequencies. Further, this X-shaped structure was utilised to design a novel TMD (X-absorber) to enhance the overall vibration suppression performance. Accordingly, multi-variable optimisation analysis was performed, and tuneable stiffness and damping properties, nonlinear influence, and vibration suppression performance of this X-absorber were systematically investigated. The X-shaped structure can provide beneficial nonlinear damping to improve the system parametric robustness and tuneable quasi-zero stiffness to significantly widen the suppression bandwidth. Moreover, in comparison to traditional absorbers, the X-absorber can successfully mitigate or eliminate potential instabilities that are inherent in Duffing systems. Based on the superior nonlinear damping and stiffness properties of this X-shaped structure, a compact X-shaped mount (X-mount) was designed with a special oblique spring for a wider quasi-zero-stiffness (QZS) range. The static analysis explores the combination effect of the negative and contact stiffness; therefore, a wider range of QZS is achieved via this combination effect. Further, the isolation performance of this X-mount is evaluated, which indicates a tuneable payload and resonant frequency property, which can be optimally designed to achieve an excellent isolation effect: lower resonance peak and wider isolation frequency range. A prototype was designed for the experimental investigation, which verifies the theoretical results, including the influence of the structural parameters, enlarged QZS range, and excellent isolation effects. The results show that this bio-inspired structure can be freely designed to have advantageous nonlinear damping and stiffness properties, which could provide feasible and promising solutions in numerous practical applications.