Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Piezoelectric devices exhibit unique properties that vary with different vibration modes, closely influenced by their polarization direction. This paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions, using a state-space-based differe...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and mechanics 2024-11, Vol.45 (11), p.1949-1964
Main Authors: Li, Zhi, Fan, Cuiying, Guo, Mingkai, Qin, Guoshuai, Lu, Chunsheng, Liu, Dongying, Zhao, Minghao
Format: Article
Language:English
Subjects:
Applications of Mathematics
Cantilever beams
Classical Mechanics
Differential equations
Exact solutions
Fluid- and Aerodynamics
Free vibration
Frequency analysis
Impact analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical methods
Partial Differential Equations
Polarization
Quadratures
Resonant frequencies
State space models
Structural design
Vibration analysis
Vibration mode
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Piezoelectric devices exhibit unique properties that vary with different vibration modes, closely influenced by their polarization direction. This paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions, using a state-space-based differential quadrature method. First, based on the electro-elasticity theory, the state-space method is extended to anisotropic piezoelectric materials, establishing state-space equations for arbitrary polarized piezoelectric beams. A semi-analytical solution for the natural frequency is then obtained via the differential quadrature method. The study commences by examining the impact of a uniform polarization direction, and then proceeds to analyze six polarization schemes relevant to the current research and applications. Additionally, the effects of geometric dimensions and gradient index on the natural frequencies are explored. The numerical results demonstrate that varying the polarization direction can significantly influence the natural frequencies, offering distinct advantages for piezoelectric elements with different polarizations. This research provides both theoretical insights and numerical methods for the structural design of piezoelectric devices.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-024-3182-9