Stationary Response of Nonlinear Vibration Energy Harvesters by Path Integration

A path integration procedure based on Gauss-Legendre integration scheme is developed to analyze probabilistic solution of nonlinear vibration energy harvesters (VEH) in this paper. First, traditional energy harvesters are briefly introduced and their non-dimensional governing and moment equations are given. These moment equations could be solved through the Runge-Kutta and Gaussian closure method. Then, the path integration method is expanded to three-dimensional situation, solving the probability density function (PDF) of VEH. Three illustrative examples are considered to evaluate the effectiveness of this method. The effectiveness of nonlinearity of traditional monostable VEH and a bistable VEH are further studied too. At the same time, Equivalent linearization method(EQL) and Monte Carlo simulation are employed too. The results indicate that three-dimensional path integration method can give satisfactory results for the global PDF, especially for the tail PDF, and they have better agreement with the simulation results than those of the EQL. In addition, the different degrees of hardening and softening behaviors of the PDFs occur when the nonlinearity coefficient increases and the bistable type is considered.