Optimal Placement of Piezoelectric Transducers for Passive Vibration Control of Geometrically Non-Linear Structures

Abstract

In this paper, an attempt is made to determine optimal location of piezoelectric transducers for passive vibration control of geometrically complicated structures and shells with non-linear curvatures. Industry-standard aircraft leading edge structure is considered for the analysis and experimental verification. Finite element model of the leading edge structure consisting of a thin layer of piezoelectric elements on the inner surface of the leading edge covering the whole surface is built and appropriate boundary conditions are applied. All the piezoelectric properties are incorporated into the elements. Modal piezoelectric analysis is performed to investigate the electric potential developed in the piezoelectric elements in the first bending and torsion modes. Location of the piezoelectric elements yielding highest amount of electric potential is identified as the best location for vibration absorption. Based on the analysis results, six piezoelectric vibration absorbers are determined to be used for performing the passive vibration control of the two modes. Results of the analysis are verified with an experimental testing of the aluminum leading edge with piezoelectric vibration absorbers firmly attached to it. A good agreement is found between the analytical and experimental results. Further, two resistive shunt circuits are designed for the passive damping of the first bending and torsion modes in which the electric potential developed would be dissipated as heat to obtain passive vibration compensation. Experimental verification of the passive damping is performed at these two modes with appropriate shunt circuits affixed to the piezoelectric vibration absorbers. Amplitude reduction around 30% and 25% and Q-factor reduction up to 15% and 10% are obtained in the bending and torsion modes, respectively. In addition, some amount of damping is observed at higher modes as well.