Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

doi:10.1007/s10483-024-3182-9

Abstract

Abstract:

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.

Key words: piezoelectric laminated beam, free vibration, arbitrary polarization, state-space equation, differential quadrature method, natural frequency

2010 MSC Number:

74H45

Zhi LI, Cuiying FAN, Mingkai GUO, Guoshuai QIN, Chunsheng LU, Dongying LIU, Minghao ZHAO. Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1949-1964.

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Figures/Tables 10

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