A second-order theory for lithium niobate piezoelectric plates with a ferroelectric inversion layer in coupled extensional, thickness-stretch and symmetric thickness-shear motions

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.