Modeling of actively damped beams with piezoelectric actuators with finite stiffness bond

The piezoelectric strain actuation of beams has been extensively studied. It is well known that a number of non-idealities may affect the performance of piezoelectric sensors or actuators. In particular, the existence of a finite stiffness bond between the actuator and the structure causes a reduction in the effectiveness (or sensitivity) of induced strain actuators (or sensors) mounted on the surface of a structure. This effect may be significant for short actuators and/or less stiff bonding layers. The objective of this work is to assess the influence of a finite stiffness bond between piezoelectric sensors/actuators and the structure on the active damping of beams subjected to rigid body rotations and elastic deformations. The depoling of the piezoelectric material is also taken into account in the model. A finite element formulation that incorporates this effect is proposed. The formulation uses an Euler-Bernoulli model for the beam and assumes the bond layer to be in a state of pure shear. The effect of the finite bond stiffness appears explicitly in the electro-mechanical coupling matrix. The present formulation includes the effect of the finite bond stiffness with good approximation without introducing extra degrees of freedom in the system. Active damping is introduced in the beam by a simple control law using rate feedback. A numerical example indicates that, within certain limits, the finite stiffness bond may be compensated for by using a higher gain in the control system. However, the finite bonding stiffness has to be taken into account when designing the control system.