ИСТИНА

There are considered the eigenvalue problems of the tensor and the tensor-block matrix of any even rank. A complete orthonormal system of eigentensors for a symmetric tensor of any even rank, as well as a complete orthonormal system of eigentensor-columns for an symmetric tensor-block matrix of any even rank are constructed in an explicit form. It is represented the elastic energy of deformation and the constitutive relations (Hooke’s law) using the introduced tensor columns and tensor-block matrix. A canonical presentation of the tensor-block matrix, the specific strain energy and the constitutive relations are given. The symbols of structure of tensor and tensor-block matrix are introduced. A classification of some anisotropic materials is given. Using the canonical representations of tensors (tensor-block matrix), it is obtained dispersion equations and expressions for dispersion tensors. Formulas for velocity of the waves for some materials through the eigenvalues of the material tensors (tensor-block matrix) are also obtained.