Identification of nonlinear piezoelectric coefficients

An identification scheme that exploits the vibration response and generated voltage of an energy harvester is proposed to estimate parameters representing nonlinear piezoelectric coefficients. We develop the governing equations of a cantilever beam with tip mass and a piezoelectric layer using the generalized Hamilton's principle and by accounting for mechanical energy, virtual work, and electric enthalpy. We then use the method of multiple scales to determine the approximate solution of the response to a direct resonant excitation. We show that the nonlinear behavior captured by the method of multiple scales as approximate solution and amplitude and phase modulation equations can be used to estimate parameters of the nonlinear piezoelectric constitutive relations.