Computer modeling of three-dimensional wave movements in anisotropic elastic environments

The theory of elastic waves in anisotropic bodies concerns to well enough investigated section of mechanics of continuous environments and the basic results in this direction belong to F. I. Fedorov, M. J. Musgrave, R. G. Payton, E. Dieulesaint, D. Royer [

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], etc. However, three-dimensional representations of wave movements (a surface of reverse velocities, wave surfaces) are absent in full, that it is possible to explain complexity and bulkiness of the corresponding characteristic equations, and also absence of their exact analytical decision (exception transversal-isotropic environments make). Researches of features of propagation of flat elastic waves and classification of anisotropic environments are lead for special directions and crystallographic planes of an anisotropic body, which not always yields true and consistent results.

The offered approach to visualization and the quantitative description of three-dimensional wave movements bases on sharing of system of computer mathematics

Mathematica

in aggregate with methods of characteristics of the theory of the differential equations with partial derivatives of hyperbolic type. Thus the basic stages of modeling of wave processes are the finding of the characteristic equation, its analytical decision, definition of velocities of propagation of elastic waves and coordinates of points of environment which energy of wave indignation has reached. The specified stages are put in a basis of the package of expansion of system Mathematica developed by authors which functionalities allow to execute construction of surfaces of velocities, reverse velocities and surfaces of ray velocities (three-dimensional wave fronts), and also to construct sections of these surfaces any plane which is passing through the beginning of coordinates for anisotropic environments of any class of symmetry.

Surfaces of reverse velocities and wave surfaces enable to carry out the strict classifications of anisotropic environments basing the simultaneous account of features two quasitransversal waves. The obtained results also can be used both for correct statement of experiments, and for correct interpretation of experimental data as allow to generate evident representations about features of propagation of waves in anisotropic environments.