ИСТИНА

Kinematic and dynamic conditions on the surface of the strong discontinuity in micropolar mechanics, the laws of conservation of mass and the tensor of internal moments of inertia, as well as the theorem of living forces and the first and second laws of thermodynamics at the wave front are given. Recording the constitutive relations of the micropolar theory of elasticity at the wave front (in jumps) and taking into account the dynamic conditions, the problem of finding of the velocities of wave propagation in an arbitrary anisotropic medium is reduced to the eigenvalue problem for the dispersion tensor-block matrix under consideration, the characteristic equation of which is the dispersion equation. As a special case, the classical medium is considered. Further, since the eigenvalues of the tensor and the tensor-block matrix are invariant quantities, therefore in this work our goal is to find the expression for the velocities of wave propagation of certain media through the eigenvalues of material tensor objects. In particular, we consider materials with the anisotropy symbol {1.5} and {5.1}, as well as isotropic materials, and for them we determine the expressions for the velocities of wave propagation. In addition, we obtained expressions for the velocities of wave propagation for materials of cubic syngony with the anisotropy symbol {1,2,3} (the matrix of the elastic modulus tensor components has three independent components), hexagonal system (transversal isotropy) with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has five independent components), trigonal system with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has six independent components), tetragonal system with anisotropy symbol {1,1,1,2,1} (the matrix of the elastic modulus tensor components has six independent components). We also obtained the expressions for the velocities of wave propagation for a micro-polar medium with the anisotropy symbol {1.5.3} and {5.1.3}, and for an isotropic micro-polar material.