Abstract:
For hypoelastic media with initial stresses, the propagation of acoustic waves is considered from the point of view of superposition of small perturbations on finite strains. The initial state of the medium is characterized by homogeneous fields of finite strains and stresses, wave propagation is described by small perturbations of the displacement field. In the article, the formulation of the theorem on the change in the kinetic energy of the medium, linearized in the vicinity of the initial state, and, as a consequence, the formulation of the acoustic Poynting theorem for a hypoelastic medium are obtained. An expression for the Umov – Poynting vector for a hypoelastic medium is written in terms of a generalized true stress tensor.
For plane monochromatic waves, the change in the stress tensor associated with the passage of a wave in a medium with initial stresses is determined, and an expression for the Umov–Poynting vector is obtained through the second Christoffel tensor and the initial stresses acting in the medium. An expression for the radial velocity vector that takes into account the initial stresses acting in the medium is obtained. It is shown that under the action of initial stresses, the Umov – Poynting vector deviates from the radial velocity vector. This result does not allow to use the radial velocity vector to determine the direction of energy flows during the propagation of acoustic waves in hypoelastic media with initial stresses.
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