The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals

Abstract

The investigation of thermoelastic wave propagation in elastic media is bound to have much influence in the fields of material science, geophysics, seismology, and so on. The heat conduction equations and bound equations of motions differ by the difficulty level and presence of many physical and mechanical parameters in them. Therefore thermoelasticity is being extensively studied and developed. In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.

The Propagation of Thermoelastic Waves in Different Anisotropic Media Using Matricant Method

“…In papers [12,13], the general form a matricant structure is similar to the (31) and the exact solution of the system of differential equations (9), which describes the propagation of thermoelastic waves in anisotropic medium was formulated. The system of differential equations is as described (23).…”

“…The wave propagation in the thermoelastic anisotropic medium have been investigated by using a matricant method, for instance wave propagation waves in liquid crystals and in thermoelastic medium [11][12][13][14][15][16][17]. In the paper [18], authors consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space.…”

Propagation of electromagnetic waves in stationary anisotropic media

“…Based on the method matriciant [12] EM wave propagation in elastic, thermoelastic anisotropic, anisotropic dielectric media, in anisotropic plates, and with magnetoelectric effect have been investigated [13][14][15][16]. The matriciant method is also employed to investigate propagation of spin waves, the waves in liquid crystals and wave propagation in thermoelastic media [17][18][19].…”

Propagation of Electromagnetic Waves in Cholesteric Liquid Crystals

“…It was shown that these SEV are effectively generated by the attenuated total reflection method. Processes in elastic anisotropic and anisotropic dielectric media and propagation of waves in anisotropic plates, electromagnetic waves in media with magnetoelectric effect [14][15][16][17], and waves in liquid crystals and thermoelastic media [18][19][20] were considered in [13] using the matricant method. Results of uniform description of wave processes in media with different physicomechanical properties were reported at the XVth All-Russian School-Seminar "Physics and Application of Microwaves" named after A. P. Sukhorukov (Waves-2016) [21].…”