Design strategy for optimizing the bandwidth of the hardening vibration generator with customized response

Abstract For popular nonlinear vibration energy harvesting systems, such as the Duffing type or the piecewise type, the stiffness profile generally follows a specific explicit expression. The response is thus determined by the coefficients of the stiffness expression and the performance trade-off between high- and low- frequency ranges always exists. To break the restriction, the non-typical nonlinear system whose stiffness profile is arbitrarily variable without an explicit expression is a promising approach. This paper proposes a novel design strategy for the hardening system to optimize the bandwidth. A customized response composed of the starting segment and the flat transition segment is firstly sketched for a target frequency range. The first segment is adopted from a linear oscillator with the rapidly increasing response while the second segment is a straight line connecting the response peak at the high cut-off frequency to the starting segment at the low-end frequency. By finding out the flattest straight line for the transition segment, the high-frequency response is ensured and the low-frequency response is maximized at the same time. Experimental tests on an elaborated prototype show that the designed generator can achieve the optimized response as desired. The superior performance due to the performance enhancement in the low-frequency range is confirmed by comparison with literature generators.