FE analysis of a PZT-actuated adaptive beam with vibration damping using a parallel R–L shunt circuit

This paper presents the simulation of adaptive structures with shunt circuits via the finite element method (FEM). The experiment configuration consists in an aluminium cantilever beam actuated by a PZT patch, whose flexural vibration is transmitted to a collocated PZT sensor, which is connected to a parallel R–L shunt circuit damping the vibration. First, starting from the piezoelectric constitutive equations, analytical formulations using FEM are defined for the actuator/beam/sensor vibrating system. Together with the corresponding sensor compliance, the connected shunt circuit is implicitly represented through an equivalent electrical load impedance. Optimal tuned values of the resistor and inductor for the shunt circuit are calculated at selected harmonic resonance vibration frequencies, and further related FE data input and boundary conditions are developed. Extensive numerical results are then obtained in using the FEM code ANSYS Multiphysics, which has piezoelectric coupling capabilities as well as electric finite elements to be used in the R–L circuit simulation. Calculated reduction levels of the beam vibration amplitude, due to the shunt circuit with optimal tuned R–L values, attain high values. Finally, an alternative method to simulating implicitly the R–L circuit consists in applying a shunt-equivalent voltage input as supplementary boundary condition to the sensor. In this method, numerical results are obtained by using the FEM code FEMLAB, with its ability of data transfer into the MATLAB script.