Dynamics and guided waves in a smart Timoshenko beam with lateral contraction

Surface-bonded wafer-type piezoelectric transducers (PZTs) have been widely used to excite or measure ultrasonic guided waves for the structural health monitoring of thin-walled structures. For successful prediction of the dynamics and ultrasonic guided waves, it is essential to use very reliable computational models for the PZT-bonded multi-layer smart structures. In this paper, the spectral element model is developed for two-layer smart beams which consist of a metallic base beam layer and a PZT layer. Axial-bending-shear-contraction coupled equations of motion and boundary conditions are derived by using Hamilton's principle with Lagrange multipliers based on the Timoshenko beam theory and Mindlin–Herrmann rod theory. The high accuracy of this spectral element model is verified in due course and the effects of a lateral contraction on the dynamics and guided wave characteristics of the example smart beams are investigated by using this spectral element model. In addition, the constraint forces at the interface between the base beam and the PZT layer are also investigated via Lagrange multipliers.