Аннотация
Free vibration problems of a flat element are investigated by all boundary value problems; generalization of the decomposition method in dynamics is given to solve boundary value problems, while it is shown that the decomposition method gives an exact solution obtained by the direct method, which in turn makes it possible to test the parts of production plants for wear leading to the shutdown of the equipment or the whole process.By checking the strength of the equipment parts, studying the degree of risk of possible breakdowns, emergency shutdowns can be predicted, and it is also possible to create controlled shutdowns.