The mathematical algorithm for analysis of piezoelectric stacks with structural damping

The work presents a proposal of mathematical algorithm developed for analysis of piezoelectric stacks that consist of classical PZT piezoelectric transducers. The considered systems vibrate longitudinally. Piezoelectric plates are combined in order to obtain multiplied displacement of the system and ensure more effective operation. Using constitutive equations of piezoelectric materials and an equation of the single plate’s motion, a matrix of characteristics of the system was obtained. The matrix of characteristics consists of relations between mechanical and electrical parameters (forces, displacements, electric current and voltage) that describe behaviour of the system. A structural damping of the plate’s material was being taken into consideration using Kelvin-Voigt model of material and its influence on the plate’s dynamic flexibility was analyzed [1, 2]. A dynamic flexibility – relation between the plate’s deformation and a force applied to the system is considered. Using the obtained dependences and non-classical methods, characteristics of piezoelectric stacks were designated and presented on charts. The obtained results were juxtaposed with characteristics of the system without structural damping.