Nonlinear dynamic analysis of asymmetric tristable energy harvesters for enhanced energy harvesting

This paper aims to reveal the nonlinear dynamic mechanism of asymmetric tristable energy harvesters and enhance the energy harvesting performance for different excitations. The general harmonic balance solutions of asymmetric tristable energy harvesters and the corresponding Jacobian matrix for estimating the stability of these analytical solutions are deduced. It is found that asymmetric tristable energy harvesters have seven analytical solutions (four stable solutions) under the appropriate excitation frequency and amplitude, which are verified by using basins of attraction. The influence mechanism of asymmetry of potential wells on energy harvesting performance is analyzed. The results show that the potential barrier is a key factor to determine the orbit height of high-energy interwell oscillations, which influences the amplitude of the output voltage. The influence essence of asymmetry on tristable energy harvesters is to change their potential wells and adjust the distribution of their potential energy. By changing the unstable equilibrium positions, a series of tristable energy harvesters with different dynamic characteristics can be obtained, which will benefit energy harvesting under various excitation conditions.