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Micromachines
Volume 16
Issue 1
10.3390/mi16010020
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Article

Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method

by
Wenxiang Ding
1,*,
Zhaofeng Liang
1,*,
Wei Zhao
1,
Hongmei Zhong
1,
Dan Chen
2,
Maxime Bavencoffe
3 and
Marc Lethiecq
3
1
School of Mechanical and Electrical Engineering, Shenzhen Polytechnic University, No. 7098, Liuxian Avenue, Shenzhen 518055, China
2
Institute of Ultrasonic Technology, Shenzhen Polytechnic University, No. 7098, Liuxian Avenue, Shenzhen 518055, China
3
GREMAN UMR 7347 CNRS, Université de Tours, INSA Centre Val de Loire, 3 Rue de la Chocolaterie, 41000 Blois, France
*
Authors to whom correspondence should be addressed.
Micromachines 2025, 16(1), 20; https://doi.org/10.3390/mi16010020
Submission received: 6 December 2024 / Revised: 23 December 2024 / Accepted: 24 December 2024 / Published: 26 December 2024
(This article belongs to the Special Issue Acoustic Transducers and Their Applications, 2nd Edition)
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Abstract

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.
Keywords: multilayer piezoelectric stack; dynamic stiffness method; electrical impedance; mode shape; finite element method multilayer piezoelectric stack; dynamic stiffness method; electrical impedance; mode shape; finite element method

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MDPI and ACS Style

Ding, W.; Liang, Z.; Zhao, W.; Zhong, H.; Chen, D.; Bavencoffe, M.; Lethiecq, M. Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method. Micromachines 2025, 16, 20. https://doi.org/10.3390/mi16010020

AMA Style

Ding W, Liang Z, Zhao W, Zhong H, Chen D, Bavencoffe M, Lethiecq M. Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method. Micromachines. 2025; 16(1):20. https://doi.org/10.3390/mi16010020

Chicago/Turabian Style

Ding, Wenxiang, Zhaofeng Liang, Wei Zhao, Hongmei Zhong, Dan Chen, Maxime Bavencoffe, and Marc Lethiecq. 2025. "Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method" Micromachines 16, no. 1: 20. https://doi.org/10.3390/mi16010020

APA Style

Ding, W., Liang, Z., Zhao, W., Zhong, H., Chen, D., Bavencoffe, M., & Lethiecq, M. (2025). Modeling and Characterization of Multilayer Piezoelectric Stacks via Dynamic Stiffness Method. Micromachines, 16(1), 20. https://doi.org/10.3390/mi16010020

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