Active damping of beams by piezoelectric system: effects of bonding layer properties

The paper is aimed at the active damping of structural vibration of a simply supported beam by using a piezoelectric, collocated sensor/actuator pair. The control concept is based on the velocity feedback. The bending-extensional dynamic model of the beam with glued piezoelements is proposed. The shear bonding layers both for the actuator and the sensor are assumed visco-elastic described by the Kelvin-Voigt material. The steady-state response of the beam loaded by a harmonic concentrated force is obtained from the solution of the boundary value problem. The boundary problem is formulated by the governing equations for the sections with and without piezoelectric patches, boundary conditions at the ends of the beam, continuity conditions between sections and the free stress conditions at the actuator and sensor edges. The influence of bonding layer parameters on the dynamic response of the controlled beam is analysed. The results in terms of frequency response of the beam transverse displacements show that the stiffness of bonding layers affects significantly the active damping efficiency. The beam vibrations can be reduced considerably for relatively stiff glue layers. The range of material damping parameter of the bonding layer, which causes an increase in the resonant amplitudes, is also indicated. A growth of stiffness as well as passive damping of the bonding layer results in a slight increase of resonance frequencies. The effect of variations in the bonding layer parameters on the shear stress distribution along the sensor and actuator is also presented and discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.