Dynamics analysis and parameter optimization of a vibration absorber with geometrically nonlinear inerters

The inerter-based dynamic vibration absorber (DVA) is a promising technique for vibration control. In most studies, the inerter is usually mounted in the same direction as that of the motion, which may not adequately reflect the vibration suppression capability and the two-terminal inertial feature of the inerter, and even weakens the performance of vibration absorbers. Considering the potentiality of improving the control performance by unconventional mounting methods, a rarely studied structure of geometrically nonlinear inerters is introduced into the vibration absorber system. This novel vibration absorber is presented to investigate the following issues, that is, the unknown coupled dynamical behavior between the complex nonlinear force with inertia, damping, and stiffness terms generated by this structure and the vibration absorber system, the possibility of vibration absorption facilitated by this structure, and the full utilization of the two-terminal inertial feature of the inerter. The approximate solutions of the system are obtained using the harmonic balance method. The influence of each variable on the system response is analyzed, and the system parameters are optimized by using the grey wolf algorithm. In addition to the ordinary resonance phenomenon, there are also dynamic features such as soft characteristic jump behavior and response loops at certain parameter range. As a nonlinear system, this model is more stable than the nonlinear energy sink (NES). The optimized amplitude-frequency curves are equal-peak stable, similar to the linear vibration absorbers. The robustness of system parameters is high for small inerter-mass ratios or excitation amplitudes, which is better than DVAs. Compared to the classical linear vibration absorber, NES, and improved NES, the vibration suppression capacity and damping bandwidth of this model are enhanced. In comparison, it is also found that this model has smaller optimum parameters than the classical NES and equivalent inerter-enhanced DVA and NES. This model offers a new solution for the design and implementation of passive vibration absorbers with comprehensive performance.