Semi-analytical free-vibration analysis of piezoelectric adaptive beams using the distributed transfer function approach

Abstract

SUMMARY A distributed transfer function (DTF) approach is proposed for the free-vibration analysis of moderately thick cantilever beams with symmetrically bonded piezoelectric patches. The piezoelectric adaptive structure is decomposed into three sections; the first and third sections contain only the bare parts of the beam before and after the patches, whereas the second section contains the beam part equipped with the piezoelectric patches bonded to its upper and lower surfaces. The analytical formulation assumes first-order shear deformation kinematics and linear electric potential through each patch thickness and uses the extended Hamilton's principle to derive the equations of motion and electromechanical boundary conditions. The latter are then transformed into a first-order state space equation using the DTF approach in order to get the short-circuit and open-circuit free-vibration problems that consider the equipotential physical conditions on the electroded upper and lower surfaces of the piezoelectric patches. The implemented DTF approach is validated by running three benchmarks from open literature. The comparison of the obtained results with those provided by three-dimensional finite elements using a commercial software shows reasonable correlation. Copyright © 2011 John Wiley & Sons, Ltd.