Theoretical analysis of multi-stable energy harvesters with high-order stiffness terms

Abstract

This paper mainly focuses on theoretical analysis of multi-stable energy harvesters with high-order stiffness terms to reveal their dynamic response mechanism and enhance energy harvesting performance. A modified Lindstedt–Poincaré method is applied to explicitly find the coupled relationship of the amplitude–frequency response equations which are consistent with the direct results from the traditional method of multiple scales. The nine-valued responses are found and five of them are stable. Meanwhile, complex multi-valued characteristics are observed in the amplitude of the response displacement. Especially, eleven types of interesting dynamic characteristics are found with the variation of the excitation amplitude. Combining with the stability analysis, the dynamic response mechanism of multi-stable energy harvesters is revealed. Furthermore, the influences of high-order nonlinear coefficients on the response are analyzed. The selection of high-order nonlinear coefficients for obtaining high-energy oscillations over a wide frequency range is analyzed.