The formulation of the acoustoelasticity problem is given on the basis of refined motion equations of orthotropic plates. These equations are constructed in the first approximation by reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of the theory of plates, where the approximation of the transverse tangential stresses and the transverse reduction stress is made with the help of trigonometric basis functions in the thickness direction. Wherein at the points of the boundary (front) surfaces, the static boundary conditions of the problem for tangential stresses are satisfied exactly and for transverse normal stress — approximately. Accounting for internal energy dissipation in the plate material is based on the Thompson—Kelvin—Voigt hysteresis model. In case of formulating problems on dynamic processes of plate deformation in vacuum, the equations are divided into two separate systems of equations. The first of these systems describes non-classical shear-free, longitudinal-transverse forms of movement, accompanied by a distortion of the flat form of cross sections, and the second system describes transverse bending-shear forms of movement. The latter are practically equivalent in quality and content to the analogous equations of the well-known variants of refined theories, but, unlike them, with a decrease in the relative thickness parameter, they lead to solutions according to the classical theory of plates. The motion of the surrounding the plate acoustic media is described by the generalized Helmholtz wave equations, constructed with account of energy dissipation by introducing into consideration the complex sound velocity according to Skudrzyk.

中文翻译：

---

精细的正交各向异性板运动方程的声弹性问题陈述

基于正交各向异性板的精细运动方程，给出了声弹性问题的公式。通过将弹性理论的三维方程简化为板理论的二维方程，可以在一阶近似中构造这些方程，借助该方程可以近似求出横向切向应力和横向减小应力。厚度方向上的三角基函数。其中，在边界（前表面）的点处，切向应力问题的静态边界条件完全满足，而横向法向应力则近似满足。板材内部能量耗散的计算基于Thompson-Kelvin-Voigt磁滞模型。如果对真空中板变形的动态过程提出问题，则将方程分为两个单独的方程组。这些系统中的第一个描述了非经典的无剪切，纵向和横向运动形式，伴随着扁平横截面变形，第二个系统描述了横向弯曲-剪切形式的运动。后者在质量和内容上实际上等同于精炼理论的著名变体的类似方程式，但是与它们不同的是，随着相对厚度参数的减小，它们导致了根据经典板理论的解决方案。平板声介质周围的运动由广义的亥姆霍兹波方程描述，