Response prediction of an energy harvesting system under the combined harmonic and random excitation

Adopting nonlinear vibrational-based energy harvesting (VEH) techniques to answer the electrical energy demands of microelectronic devices has become commonplace. Considering the complex service environment of these devices, it is necessary to model VEH systems that closely resemble their real operational conditions. This will facilitate more precise prediction and analysis of the energy harvesting efficiency. The combined periodic and random excitation effectively simulate the real operating environment of VEH systems, but systematic research on VEH systems is usually limited to periodic excitation or random excitation. This paper employs the Radial Basis Function neural networks (RBFNN) method to solve the transient response of a VEH system subjected to combined harmonic and Gaussian white excitations. This technique initially constructs a trial solution composed of Gaussian basis functions and time-varying weight coefficients for the Fokker-Planck-Kolmogorov (FPK) equation. Subsequently, the finite difference method is employed to discretize the time derivative terms, constructing a loss function composed of the residuals of the FPK equation and the constraint conditions of weight coefficients. Lastly, the loss function is minimized to obtain the optimal matrix of weight coefficients, allowing for the determination of the optimal trial solution for the probability density function of the transient response. The monostable and bi-stable systems are taken as examples to verify the solution scheme, and the effects of electromechanical coupling coefficients and the ratio between the mechanical and electrical time constants on the transient response and output power of the system are investigated. The semi-analytical solutions are rigorously validated with Monte Carlo simulation. The main conclusions are as follows: under combined periodic and random excitations, the topological structure of the probability density function of system response undergoes significant changes over time. Stochastic jump and stochastic P-bifurcations are induced by changes in critical parameters of the system, and parameter variations have a pronounced impact on the efficiency of energy harvesting. The findings of this work provide theoretical references for exploring the stochastic dynamical evolution of VEH systems and optimizing the efficiency of energy harvesting. © 2024 Chinese Academy of Sciences. All rights reserved.