APPLIED PROBLEMS OF NATURAL VIBRATIONS OF A PLATE AS A PLANE ELEMENT INTERACTING WITH THE ENVIRONMENT.

Abstract

Abstract: an urgent problem of theoretical research in the field of non-stationary oscillations of elastic and viscoelastic bodies is the development of a strictly mathematical approach to the study of two-dimensional and spatial problems. The main goal of studying the non-stationary behavior of various elements of structures and structures in this work is reduced to a rigorous and justified formulation of the boundary value problems of vibrations and wave processes in deformable media.Based on the method developed in the works of I.G. Filippov, the article is devoted to the mathematical formulation of boundary value problems of vibrations of elements of structures and structures. A technique has been developed for calculating the frequencies of natural vibrations of flat elements under various conditions of their fixing. Practically important tasks in the field of construction practice have been solved. The creation of new construction technologies, the use of qualitatively new materials puts forward increased requirements for the dynamic behavior of deformable media.The obtained theoretical and applied results make it possible to solve a wide class of practical problems of oscillations of elements of structures and structures, and is confirmed by a rigorous mathematical formulation of problems, verification and comparison with classical theories of oscillations and other theories of recent years.