Nonlinear piezoelectric shunting for structural damping

The electromechanical coupling behavior of piezoelectric materials allows their use as damping elements in dynamic structural systems. By shunting the electrical terminals of a piezoelectric element bonded to a structure, electrical components can be used to change the apparent dynamic response of the structure. Linear shunting components such as resistive elements or inductive-resistive-capacitive circuits, respectively, have been used to produce behavior analogous to that use of viscoelastic damping materials and tuned proof-mass dampers. This paper examines the possible use of nonlinear shunting circuits with the aim of attaining higher effective damping levels and reduced sensitivity to frequency tuning as compared with conventional linear shunts. The shunting components may be realized in such a way as to allow the vibrational energy removed from the structure to be recovered in a usable form. The shunting circuits examined in this work are a rectified DC voltage source and a time-varying resistor. A one-dimensional electromechanical circuit model is used to evaluate the performance of the shunts in terms of effective material loss factor, and the dependence of this loss factor on the electromechanical coupling coefficient and the disturbance amplitude is considered. The behavior of the rectified DC voltage source shunting scheme applied to a simple resonant structure is examined to determine the achievable damping levels, amplitude dependence, and potential undesirable motions induced at higher harmonics of resonance or disturbance frequencies by the electrical nonlinearities.