Dynamic Modeling and Structural Optimization of a Partially Laminated Piezoelectric–Metal–Piezoelectric Actuator

:Piezoelectric actuators are core components in precision motion control due to their unique electromechanical coupling properties. This paper establishes a dynamic model for a partially laminated piezoelectric–metal–piezoelectric beam actuator based on the Euler–Bernoulli beam theory. The model comprises symmetrically bonded piezoelectric layers on both sides of a central metal substrate, with the piezoelectric material partially distributed along the beam length. The structure is analyzed segment-wise along the beam’s longitudinal length direction. By applying continuity conditions at the interfaces of varying cross-sections and leveraging the structural symmetry, analytical solutions for both the natural frequency and output displacement are derived. The analytical predictions are validated against finite-element results, and experiments also verify the accuracy of the analytical solution of the analytical voltage–displacement response. In addition, the effects of key geometric parameters on the dynamic performance are systematically investigated. The proposed model provides theoretical guidance for tuning the resonance characteristics and drive displacement design of the PMP actuators.