The Problem of Eigenvalues of Material Properties Tensor Objects and Velocities of Wave Propagation in the Structures

Nikabadze, M.; Matevossian, H.; Ulukhanian, A.

Авторы: Mikhail Nikabadze, Hovik Matevossian, Armine Ulukhanian
Сборник: PROGRAMME & BOOK OF ABSTRACTS of International Scientific Workshop «Related Problems of Continuum Mechanics»
Тезисы
Год издания: 2019
Место издания: AKAKI TSERETELI STATE UNIVERSITY Kutaisi, Georgia
Первая страница: 20
Последняя страница: 20
Аннотация: The problems of eigenvalues of the tensor and the tensor-block matrix of any even rank are considered. 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 the 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 using the introduced tensor columns and tensor-block matrix. The canonical representations of the tensor-block matrix, the specific strain energy, and the constitutive relations are given. The symbols of the structure of the 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 the velocity of the waves for some materials through the eigenvalues of the material tensors (tensor-block matrix) are also obtained.
Добавил в систему: Никабадзе Михаил Ушангиевич

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