Analytical Method of Investigation of Wave Processes in Mathematical Models of Some Dynamic Systems

The mathematical model of two-dimensional body oscillations with given profiles and stresses at two moments of time is proposed. The method of research of this model, in particular, in the case of longmeasuring systems is developed. The oscillatory processes are simulated by a two-point in time problem for a wave equation in an unbounded domain. A class of existence of a unique solution of a problem is established and an exact method of constructing a solution is proposed. Also, there is carried out the investigation of specific models of wave processes, which show the effectiveness of the developed method.