Nonlinear piezoelectric vibration absorbers

The effect nonlinear electrical shunts on the performance of piezoelectric vibration absorbers for linear systems is presented. The equations of motion are derived in a format suitable for perturbation analysis. An electrical shunt containing cubic and quadratic elements is coupled to the structure via the piezoelectric effect. Nonlinearities are introduced as a combination of the square and/or cube of the charge flowing in the linear inductive-resistive (LR) shunt. Turning the shunt near a structural mode causes mechanical energy to be transformed to electric energy and dissipated by the resistive element in the shunt in a manner analogous to a damped vibration absorber. Analysis is carried out using the method of multiple scales. Simulation results are also presented.