Electromechanical coupling model of variable-section piezoelectric composite beams in longitudinal vibration

The traditional step-reduction method is popular for modeling mechanical vibration of variable-section homogeneous beams (VHBs). However, this method cannot transfer electrical information and cannot depict electromechanical coupling behaviors of variable-section piezoelectric composite beams (VPCBs) in longitudinal vibration. To solve this defect, considering the structural continuity and parallel circuit factors, we propose the electromechanical step-reduction method for VPCBs. Longitudinal vibration transfer equations, linking input and output state vectors, are first created for VPCBs according to the proposed method. Then, a piezoelectric actuator excited by a VPCB is designed as a case study. Its transfer matrix model, involving mechanical and electrical properties, is developed to prove the correctness of the proposed method and the created transfer equations. Besides, an actuator prototype was manufactured for experimental verifications. The calculation results show that the longitudinal vibration frequency and velocity tend to be stable with the increase of the division number n. Their velocity vibration shapes are also consistent with each other. The calculated and experimental impedance curves have the same trend. The minimum and maximum impedance differences between the calculated and experimental are 107 ohm and 127 ohm, respectively. Finally, the modeling differences between the traditional and electromechanical step-reduction methods are compared and discussed in detail. The proposed method is more applicable to the modeling of VPCBs, which provides a theoretical tool for optimizing the excitation of the longitudinal vibration.