Calculation of characteristics of nonlinear normal waves in plates of lithium niobate for the designing of acousto-electronic devices

Abstract

The research of anharmonic effects is essential for the design of nonlinear acousto-electronic devices. Such effects involve the generation of nonlinear second harmonics in propagation of normal electroelastic waves in crystal plates. Thereby the analytical and numerical technique of the analysis of small nonlinear anharmonic effects in distribution of normal electroelastic waves in the layer of a trigonal piezocrystal of lithium niobate with thin short-circuited electroсonductive coverings of sides has been developed. The research is based on the model of physically and geometrically nonlinear electroelastic deformation with finite deformations and Gibbs's function that includes quadratic and cubic components on deformations and characteristics of intensity of quasistatic electric field. The analysis of nonlinear wave effects is build on the representation of characteristics of a normal electroelastic wave in the form of the sum of summands, which are proportional to the powers of the small parameter. The analytical form has been received for the representations of functions of the elastic displacements, intensity, induction of quasistatic electric field in nonlinear second harmonics for the studied waves from the different modes of the dispersive spectrum. Quantitative estimates have been researched for the amplitude levels of second harmonics for normal electroelastic waves with variable frequencies.