Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator

This paper provides a basic mechanics model for the flexural analysis of a sandwich beam coupled with a piezoelectric layer. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The distribution of the piezoelectric potential is obtained by including the Maxwell equation in the formulation. Based on the results of vibration analysis, it is shown that the dynamic characteristic of the entire structure is related to the position of the piezoelectric layer. More importantly, the mode shape distribution of the electric potential in the piezoelectric layer in the longitudinal direction is related to the transverse displacement, or more accurately the curvature, of the sandwich beam, and the latter is dependent on the boundary conditions. Hence, the commonly adopted assumption of uniform electric potential in the longitudinal direction needs to be carefully re-examined. The distribution of electric potential obtained serves as a guide for selecting the trial function for the mode shapes of the electric potential required in numerical methods, such as FE modelling, for coupled piezoelectric structures.