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.

The biceps brachii role in the stabilization of the cross punch

Purpose: starting from an injury background, we assumed that the biceps brachii’s activations could have an important role in upper limbs injury. In this work we analyzed whether different activations of the biceps brachii impact on the power transfer of the punch and how boxers of different skill levels activate the biceps brachii when deliver a punch according to their skill level and efficacy. Methods: we enrolled, basing on official rankings, 23 skilled (n=6) and unskilled boxers. Subjects were instructed to perform three cross punches directed to a fixed elastic target triggered by the coach whistling, and were monitored through a surface electromyography sensor (EMG) on the biceps brachii to estimate the muscular activation during the performance, and through an accelerometer placed inside the elastic impact target to estimate the impact energy. We analyzed the oscillatory content of the EMG signal in order to assess the muscular activation between skilled and unskilled boxers, and between weak and strong punches. Results: both skilled and unskilled boxers threw strong, medium and weak strikes. Skilled boxers performed better than unskilled boxers (47% vs 25% in the “strong punch” category).The EMG analysis revealed a significant increase of lower and higher frequencies (2-4 Hz and 15-17 Hz) and a decrease on the medium frequencies (7-9 Hz) in the skilled boxers compared to the unskilled boxers in strong punches. Weak punches had a similar activation patterns in the two groups. Conclusions: our results support the hypothesis that skilled boxers adapt their activation pattern of the biceps to better stabilize the punch delivery (and thus increasing the transfer of force).