Estimate of chaotic threshold of tristable vibration energy harvesters

Abstract

Tristable vibration energy harvesters own excellent energy harvesting performance, which has been verified theoretically and experimentally. Obviously, the response mechanism of an asymmetric tristable vibration energy harvester is more complex than a symmetric bi-stable vibration energy harvester. The ambient vibrations have a great impact on the harvester. Due to the complexities and the lack of analytical solutions, the streamlined design methodologies are inhibited. To facilitate future innovation and research on asymmetric tristable vibration energy harvester, this paper uses Melnikov function and modified Lindstedt-Poincaré method are adopted to study the asymmetric tristable vibration energy harvester which has higher order nonlinear terms in the dynamic equation. Analytical results are consistent with numerical simulation results. The paper uses chaotic dynamical theory to provide a simplified analytical framework for which the deeper insight into the performance of the tristable vibration energy harvester can be obtained.