Finite element model of a beam with a piezoceramic patch actuator

Piezoceramic wafer (patch) actuators have been used for the excitation and control of vibrations of beam and plate-like structures. Precise constitutive modelling of the system is important for accurate computer simulation. In this paper, a finite element model of a beam with a piezopatch actuator adhered to it is presented. Both the beam and the patch actuator are modelled using Timoshenko beam theory. Constraints are introduced to ensure continuity of the axial and transverse displacements at the interface of the two Timoshenko elements. This formulation allows the cross-section of each layer to rotate individually, which increases the accuracy compared to conventional formulations in the literature. The displacement field of the system is presented in a factored matrix form, which is utilized to derive the element mass and stiffness matrices. Theoretical and experimental frequency response functions of a piezopatch and beam system are obtained with the piezopatch electrically open and closed circuited. Better agreement is observed between the presented model and experimental results than is obtained using a Euler–Bernoulli formulation for both layers or Timoshenko theory for only one layer and Euler–Bernoulli theory for the other. The piezoelectric and dielectric behavior of the piezoceramic wafer are included in the element model. An optimized vibration absorber using an electrical resistive-inductive shunt circuit on the piezopatch is also simulated.