Vibration energy transmission in coupled systems with local nonlinearities - Shi, Baiyang (2020)
The vibration power flow analysis (PFA) has been widely accepted to investigate the dynamic performance in linear dynamical systems; however, the vibration transmission behaviour and power flow characteristics of many nonlinear dynamical systems are still unclear. This study aims to investigate the vibrational energy and power transmission in coupled systems with different types of local nonlinearities. Different approaches including analytical, semi-analytical, and numerical methods are used to gain physical insights into the power flow mechanisms of nonlinear systems. The findings are expected to provide guidelines for exploiting nonlinear elements in mitigation of power transmission and suppression of vibration to achieve enhanced designs. The effects of different nonlinearities on dynamic response, kinetic energy, and power transmission in coupled nonlinear/linear oscillators through nonlinear/linear interface are investigated. It is shown that the hardening, softening, and double-well stiffness nonlinearities and the cubic damping nonlinearity mainly affect the power flow curves locally in the vicinity of the resonant frequencies. It is found that the coupled systems with double-well potential stiffness may exhibit chaotic and super-/sub-harmonic response. Multiple solutions and jump phenomenon of vibration power transmission are also observed. The dynamic characteristics and vibrational power transmission behaviour of coupled systems incorporating bilinear stiffness and bilinear damping elements are investigated. It is observed that the bilinear spring element may cause large super-/sub-harmonic components in the response, resulting in higher level of vibration transmission through the interface. It is shown that a combination of small bilinear stiffness ratio and a large bilinear damping ratio may be employed to provide good overall suppression of vibration transmission through the nonlinear interface. Study of tuned inerter damper coupled to a linear and nonlinear primary oscillator is presented. The optimal stiffness and damping ratios to achieve equal resonant peaks of displacement and kinetic energy of the primary oscillator are obtained. It is shown that an increase in the inertance of the absorber substantially reduces the response peaks of the primary system. Nonlinearly coupled oscillators with dual-force excitations with different fundamental frequencies are studied. For the cubic stiffness interface, the stiffness nonlinearity mainly affects the secondary resonant peaks. For the bilinear stiffness interface, a larger bilinear frequency ratio shifts the secondary resonances and critical frequency of the equilibrium point of power transmission to higher frequencies. These results and findings provide a deep understanding of power generation, transmission, and dissipation mechanisms in coupled systems with local nonlinearities. This study also presents some guidelines for the designs of nonlinear systems achieving better dynamic performance.