Global Dynamics and Optimal Design of a New Highly Efficient Nonlinear Energy Sink Based on Magnetic-Elastic Impacts with Negative Stiffness

A new highly efficient elastic-impact bistable nonlinear energy sink (EI-BNES) based on magnetic-elastic impacts with negative stiffness and bistability is proposed and optimized through global dynamical analysis. The EI-BNES has better robustness and higher energy dissipation rates with nearly more than 96.5\% for broadband impulsive excitations than the traditional cubic NESs and single bistable NESs. The structure of negative stiffness impacts is realized by reasonable layout of permanent ring magnets and springs. A two-degree-of-freedom (two-DOF) elastic-impact system is established to describe the coupled nonlinear interaction between the main structure and the attached EI-BNES. A global Melnikov reduction analysis (GMRA) is proposed to study global dynamics and homoclinic bifurcations of the reduced two-dimensional subsystem, which is used to explain the mechanism of nonlinear targeted energy transfer (TET) and detect the threshold of impulsive amplitudes of EI-BNES for in-well and compound motions between in-well and cross-well resonance responses. A special type of saddle-center equilibrium points is also found in the non-smooth system of the EI-BNES and can be used to effectively increase the energy dissipation rates. The optimal design criterion of the tuned EI-BNES for better dissipation performance is also first discussed based on the GMRA and numerical techniques for calculating the Melnikov function of the non-smooth systems. The effectiveness of the analytical GMRA is also verified by numerical simulations.