# The Mathematical Algorithm for Analysis of Piezoelectric Stacks with Structural Damping

## Abstract:

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.

## Info:

Periodical:

Solid State Phenomena (Volumes 220-221)

Main Theme:

Edited by:

Algirdas V. Valiulis, Olegas Černašėjus and Vadim Mokšin

Pages:

385-390

Citation:

A. Buchacz et al., "The Mathematical Algorithm for Analysis of Piezoelectric Stacks with Structural Damping", Solid State Phenomena, Vols. 220-221, pp. 385-390, 2015

Online since:

January 2015

Authors:

Keywords:

Export:

Price:

\$38.00

Permissions:

[1] A. Buchacz, M. Płaczek, A. Wróbel, Control of characteristics of mechatronic systems using piezoelectric materials, Journal of Theoretical and Applied Mechanics 51 (2013) 225–234.

[2] A. Wróbel, Kelvin Voigt's model of single piezoelectric plate, Journal of Vibroengineering 14(2) (2012) 534–537, ISSN 1392-8716.

[3] A. Buchacz, D. Galeziowski, Synthesis as a designing of mechatronic vibrating mixed systems, Journal of Vibroengineering 14(2) (2012) 553–559.

[4] A. Buchacz, M. Płaczek, Selection of Parameters of External Electric Circuit for Control of Dynamic Flexibility of a Mechatronic System, Solid State Phenomena 164 (2010) 323–326.

[5] E. Macha, S. Braun, Editorial Statement: Current research highlighting interdisciplinary aspects of piezoelectric technologies in integrated systems, Mechanical Systems & Signal Processing 36(1) (2013) 1–6.

[6] A. Buchacz, M. Płaczek, The analysis of a composite beam with piezoelectric actuator based on the approximate method, Journal of Vibroengineering, 14(1) (2012) 111–116.

[7] K. Jamroziak, M. Bocian, M. Kulisiewicz, Effect of the attachment of the ballistic shields on modelling the piercing process, Mechanika, 19(5) (2013) 549-553.

[8] A. Buchacz, M. Płaczek, The approximate Galerkin's method in the vibrating mechatronic system's investigation, in Proceedings of The 14th Int. Conf. Modern Technologies, Quality and Innovation ModTech 2010, May 20–22, 2010, Slanic Moldova, Romania, p.147.

[9] A. Buchacz, M. Płaczek, A. Wróbel, Modelling and analysis of systems with cylindrical piezoelectric transducers, Mechanika 20(1) (2014) 87–91.

[10] A. Buchacz, M. Płaczek, A. Wróbel. Modelling of passive vibration damping using piezoelectric transducers – the mathematical model, Eksploatacja i Niezawodnosc – Maintenance and reliability 16(2) (2014) 301–306.

[11] M. Płaczek, Dynamic characteristics of a piezoelectric transducer with structural damping, Solid State Phenomena, 198 (2012) 633–638.

[12] K. Białas, Passive and active elements in reduction of vibrations of torsional systems, Solid State Phenomena 164 (2010) 260–264.

[13] A. Dymarek, T. Dzitkowski, Method of active synthesis of discrete fixed mechanical systems, Journal of Vibroengineering 14(2) (2012) 458–463.

[14] S. Zolkiewski, Damped vibrations problem of beams fixed on the rotational disk, International Journal of Bifurcation and Chaos 21(10) (2011) 3033–3041.

[15] A. Buchacz, A Wróbel, Computer-aided analysis of piezoelectric plates, Solid State Phenomena 164 (2010) 239–242.