| Abstrakt: |
Linear non-stationary dynamic problems describing transient wave processes in deformable solids are considered under the assumption that the perturbation propagation region is limited. The statement of the problem is formulated in a generalized form, it is understood that the linear constitutive relations can express the interconnection of the parameters of the stress-strain state with the temperature field, with the electric and magnetic fields and other physical characteristics. In addition, it is assumed that the material of the body can have viscoelastic properties in the framework of the linear Boltzmann-Volterra model. The integral Laplace transform with respect to time is applied to the equations and boundary conditions, taking into account the initial conditions. A theorem is formulated and proved. This theorem establishes a connection between the branch points on the complex plane of the solution of the non-stationary problem in images and the properties of the spectral set of the problem of free vibrations of the body under consideration, as well as the initial data of the non-stationary dynamic problem. The established property of solutions to the problems of the type under consideration in images in many cases facilitates the process of constructing solutions in the originals. An example illustrating the formulated theorem is given. [ABSTRACT FROM AUTHOR] |
