A second-order theory for lithium niobate piezoelectric plates with a ferroelectric inversion layer in coupled extension
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O R I G I NA L PA P E R
Dejin Huang
· Jiashi Yang
A second-order theory for lithium niobate piezoelectric plates with a ferroelectric inversion layer in coupled extensional, thickness-stretch and symmetric thickness-shear motions Received: 1 January 2020 / Revised: 14 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A second-order plate theory for a lithium niobate piezoelectric plate with a ferroelectric inversion layer is established. The theory describes coupled extensional, thickness-stretch and symmetric thickness-shear motions of the plate. The two-dimensional theory obtained is validated by comparing the dispersion relations of the relevant waves with the three-dimensional exact theory. For long waves with small wave numbers, the dispersion curves obtained from the plate theory and the three-dimensional theory have the same cutoff frequencies and curvatures. Therefore, the plate theory is useful in the design of devices operating with these waves. A piezoelectric gyroscope based on symmetric thickness-shear modes is analyzed as an example.
1 Introduction Relatively recently, it has been shown that in a piezoelectric plate of lithium niobate (LiNbO3 ) or lithium tantalate (LiTaO3 ) a layer with ferroelectric domain inversion can be created by heating one side of the plate at a temperature above the Curie point of the crystals [1,2]. The ferroelectric inversion layer grows gradually when the plate is heated and the domain boundary ultimately stops near the middle plane of the plate after a sufficiently long heat treatment. Ferroelectric plates with such a ferroelectric inversion layer offer various new possibilities for piezoelectric devices [3–12]. Specifically, these plates are particularly convenient for electrically exciting or detecting two families of acoustic modes or mechanical deformations widely used in acoustic wave devices and electromechanical transducers/sensors. One is coupled flexure and the first-order thickness shear (TS1) which is antisymmetric about the plate middle plane. The other is coupled in-plane extension and thickness stretch (TSt) as well as second-order thickness shear (TS2) which is symmetric about the plate middle plane. The first family of flexure and antisymmetric thickness shear was treated systematically in [13]. In this paper, we study the second family of extension, thickness stretch and symmetric thickness shear. Due to the material anisotropy of piezoelectric crystals and their electromechanical couplings, the analysis and design of piezoelectric devices usually present considerable mathematically challenges. For devices made from piezoelectric plates, relatively few results can be obtained from the three-dimensional (3-D) equations of piezoelectricity. Most theoretical analyses rely on approximate, two-dimensional (2-D) plate equations. There is a continuous effort on developing 2-D equations of piezoelectric plates for different applications when the plates are used in different deformation or vibration modes, e.g., [14–17]. More ref
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