Bending vibration transfer equations of variable-section piezoelectric laminated beams

The model prediction is one of the adequate approaches to evaluate the bending vibration suppression of variable-section piezoelectric laminated beams (VPLBs). Nevertheless, the changing section and the coupling between stress and electric fields bring difficulties to the bending vibration calculation. To solve the above issues, we deduce the bending vibration transfer equations of VPLBs by the transfer matrix method and the step -reduction method. The VPLBs are approximated as a combination of several constant-section piezoelectric laminated beams (CPLBs). First, the bending vibration transfer equations of the CPLBs are derived using the Timoshenko beam theory and the constitutive properties of PZTs. Then, the transfer conditions between the two adjacent CPLBs are formulated according to the mechanical and electrical connections. Finally, the bending vibration transfer matrix of the VPLB is created by assembling transfer matrixes of inner CPLBs in sequence. To verify the feasibility of the developed bending vibration transfer equations, a piezoelectric actuator and a piezoelectric cantilever beam are designed as modeling examples. The experiment investigations and finite element simulation are carried out to validate the transfer matrix models of the two modeling examples, respectively. The multi-group comparison results show that the proposed transfer equations comprehensively describe the bending vibration characteristics of the VPLBs.