Application of Stochastic Averaging to Vibrating Electro-mechanical Systems for Piezoelectric Energy Harvesting

Electro-mechanical systems are ubiquitous in engineering. For example, they are used in energy harvesting systems to convert random mechanical excitations into usable electrical power. The analysis and design of these electro-mechanical systems is particularly challenging, because concepts and methods of stochastic analysis and nonlinear dynamics are required. In this work we present a methodology for the analysis of nonlinear electro-mechanical systems with small internal friction, and subject to random external mechanical excitations. The method is based on the combined application of a model order reduction technique, to reduce the number of dynamical variables, thus reducing the complexity, and of stochastic averaging, to calculate statistical relevant quantities, and in particular expectations of the output electrical variables. As an example, we apply the proposed technique to the analysis of a piezoelectric energy harvesting system.