Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method

Multilayer piezoelectric stacks, which are multiple layers of piezoelectric materials placed on top of each other, are widely used to achieve precise linear movement and high-force generation. In this paper, a dynamic stiffness (DS) method for the dynamic vibration analysis of multilayer piezoelectric stacks is presented. First, the general solutions for all physical quantities of the three vibration contributions (i.e., pure vibration, symmetrically coupled vibration, and anti-symmetrically coupled vibration) are derived from the governing equations of motion. Then, the DS matrices of each layer of the piezoelectric stack are obtained, and they are assembled to form a global DS matrix. The electrical impedances and the mode shapes of a piezoelectric stack consisting of two piezoelectric disks connected in series and in parallel are calculated using our method as well as by the finite element method. The comparison shows good agreement. Finally, the effect of the number of layers on the dynamic responses of piezoelectric stacks is investigated. The DS method developed here provides an efficient and accurate analytical tool for the parametric and optimization analysis of the coupled vibrations of multilayer piezoelectric structures.