<title>Finite element analysis of passive piezoelectric damping tuned by using electrical impedance</title>

Abstract

Possibility of passive piezoelectric damping based on a new shunting parameter estimation method is studied using finite element analysis. Piezoelectric device with shunt electronic elements, for example, inductor and resistor, are normally used for passive piezoelectric damping to achieve damping near resonance of the target structure. The key in implementation of such an electronic damping is to tune the shunt parameters accurately. The adopted tuning method is based electrical impedance that is found at piezoelectric device and the optimal criterion for maximizing dissipated energy at the shunt circuit. Full three dimensional finite element model is used for piezoelectric devices with cantilever plate structure and shunt electronic circuit is taken into account in the model. Electrical impedance is calculated at the piezoelectric device, which represents the structural behavior in terms of electrical field, and equivalent electrical circuit parameters for the first mode are extracted using PRAP(Piezoelectric Resonance Analysis Program). After the shunt circuit is connected to the equivalent circuit for the first mode, the shunt parameters are optimally decided based on the maximizing dissipated energy criterion. A cantilever beam example is taken to demonstrate the piezoelectric damping in the finite element simulation. Less than 10 dB vibration reduction at the tip of the beam is achieved by the piezoelectric damping. When the electrical potential at the shunted electrode is simulated nearly 80 Volt was found at the first resonance frequency. The dissipated electrical power ratio with respect to the mechanical input power is calculated from this electrical voltage, and it was found to be 0.39, which is close to the energy ratio found from the electromechanical coupling coefficient of the piezoelectric patch. Since this tuning method is based on electrical impedance calculated at piezoelectric device, multi-mode passive piezoelectric damping can be implemented for arbitrary shaped structures.