On Determination of Wave Velocities through the Eigenvalues of Material Objects

Abstract

The statement of the eigenvalue problem for a tensor–block matrix of any order and of anyeven rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrixare invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities ofwave propagation of some medias through the eigenvalues of the material objects. In particular, weconsider the classical and micropolar materials with the different anisotropy symbols and for themwe determine the expressions for the velocities of wave propagation through the eigenvalues of thematerial objects.

Keywords

• eigentensor
• tensor-operator
• tensor–block matrix operator
• tensor–block matrix
• wave velocities
• dispersion tensor
• symbol of anisotropy
• velocity tensor