Response determination of a nonlinear energy harvesting device under combined stochastic and deterministic loads

An approximate analytical technique for determining the response statistics of a nonlinear piezoelectric energy harvesting device is proposed. This is attained by resorting to a recently developed method for determining the response of multi-degree-of-freedom dynamical systems with singular matrices subject to combined deterministic and stochastic loads. Such systems are often met in engineering applications, for instance, as a result of modeling the governing equations of motion of complex multi-body systems by utilizing dependent coordinates. In this regard, the governing equations of the harvesting system dynamics are treated separately. Specifically, the harmonic balance method is used for treating the deterministic component of the response, while the corresponding stochastic response component is treated by combining the stochastic averaging and the statistical linearization methodologies. A numerical example is used to demonstrate the validity of the proposed technique. The obtained results are verified by using pertinent MCS data.