Variety of Surface Actions in Problems of Surface Control of the Three-Component Electroacoustic Waves in a Piezoelectric Waveguide. Non-Acoustic Surface Actions

Abstract

The formulation of the problem of surface control of an electroactive unidirectional multicomponent elastic wave propagation in an infinite piezoelectric waveguide over a finite time interval is discussed. Based on the conditions for conjugation of electromechanical fields on the surface of piezoelectric media, as well as on the nature of possible surface electromechanical effects, a variety of surface dynamic effects is considered through the components of the elastic displacement vector, the mechanical stress tensor, the tangential component of the electric field strength and the normal component of the electric field displacement. The possibility of setting the control problem in the case of three-component electroacoustic waves depending on the anisotropy of the piezoelectric material of the waveguide is studied. The anisotropy of a piezoelectric medium leads to the formulation of an initial-boundary mathematical problem for controlling the motion of a multicomponent system. The variety of surface actions leads to the formulation of heterogeneous initial-boundary mathematical problems with surface actions of the first kind, with surface actions of the second kind, as well as for the case of mixed surface actions. An invariant record of heterogeneous initial-boundary mathematical problems is proposed in the form of a system of inhomogeneous quasi-static electro-elasticity equations, with homogeneous boundary conditions and inhomogeneous conditions of the initial and final states.