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There are the insufficiently known phenomena, resulting in the operating damages of knots and details of machines, among that most dangerous are a friction, wear, and dynamic tiredness. They behaves to the mechanical systems, the elements of that are bound by inter se forces of dry friction, that is widely widespread in a technique, especially in the knots of contact of elements with a friction. It results in the origin of new effects the account of that is needed for providing of increase of reliability of work of machines and mechanisms. At the decision of practical tasks usually use the simplified charts that are characterized the eventual number of degrees of freedom, although the real mechanical system has an endless large number of degrees of freedom. The study of vibrations of the mechanical systems on such models allows to get basic conformities to law of influence of interesting factors on dynamic descriptions of the system. In the theory of vibrations are of interest research of questions of cooperation of forces of friction, operating in the system, and force vibrations. However paid attention to the question of influence of forces of friction on the size of frequency of resonant vibrations of the mechanical systems. Under the inlaid constructions we understand such, when one elements of construction are located into other and here constrained inter se on opposite surfaces by forces of dry friction. The selection of class of the inlaid constructions, among the nonlinear mechanical systems, requires the row of clarifications. Consists the feature of design of one mass models of the inlaid constructions in that they have two degrees of freedom. It results in appearance at the inlaid constructions of new properties, what and dedicated hired.

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