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The method of creation of mathematical models of the mechanical oscillatory systems which are turning on in the structure mechanisms with kinematic couples of slippage is offered. It is shown that introduction of mechanisms can be interpreted as introduction to initial model of the additional feedback, in general, to steering on absolute speedup and on an absolute deviation. A basis of the offered technology of creation of mathematical models are representations that in the presence of the mechanism or a mechanical chain of other look power and kinematic indignations form various structures of dynamic interactions. The analytical ratios defining dynamic properties of systems are received. The features of dynamic properties which are shown in various forms of dynamic interactions and frequency characteristics are considered.

Method of construction of mathematical models is offered for mechanical systems with additional feedback ties which formed of lever mechanisms of different kinds. It shown that mathematical models can be get by simplifying more complicated system in which lever ties are realized of rigid body with fixed pivot point. Lever ties at the preparation of a model formally appear at decrease inertial moment of intermediate rigid body to very small values. It shown that mechanical oscillation system can be reduced to equivalent scheme which matches estimation scheme of chain type. Equivalent estimation schemes can to differ of various kinds of between-partial ties. Possibilities of using quasi-springs in equivalent estimation schemes are offered and justified. These complicated compositions consist of elastical elements which interconnected of lever mechanisms. Coerced stiffness’s of quasi-springs defined on rules of transformation of structural mathematical models. Base of mathematical modeling is using method of transformation of Laplas with following construction of equivalent in dynamical attitude of structural schemes of automation control systems. Analytical ratios are given. They characterize possibilities of special dynamical regimes.

Possibilities of expansion of settle of typical elementary links of mechanical oscillation systems are considered. As examples of links for transformation of movement the screw and level mechanisms are offered. Introduction of new links is equivalent of elementary links with transfer function of differential of second order. The method for definition of parameters of dynamical absorbtions of oscillation are offered.

Fragments of system,quasi-spring,in particular,can also possess zero rigidity that is shown through features of joint movements of elements of system. Results of researches are confirmed by computing modeling; schedules of frequency dependences for the relations of coordinates of the movement are provided.A number of analytical ratios for determination of frequencies of boundary conditions of transition to the different modes is received.For an assessment of dynamic properties structural mathematical models and rules of their transformation are used.

Features of interaction of elements of a dynamic quencher of oscillations in the form of a rigid body with two degrees of freedom are considered. It is shown that the dynamic quencher is interpreted in structure of mechanical oscillatory system with object of protection as additional negative tie which can be presented by the generalized spring. Dynamic ruggedness of the generalized spring depends on the frequency of external indignation and defines manifestations of dynamic properties, characteristic for the modes of dynamic blanking out of oscillations. The generalized spring possesses properties of a quasi-spring that creates possibilities of various transformations of structure of system. Introduction of concept of the generalized transmission ratio of the lever ties arising between coordinates of the movement of elements of a dynamic quencher is offered. Forms of the transfer relations of lever ties are in univocity with system of the chosen coordinates. The transfer relations of lever ties allow to detail forms of mutual movements of elements of system. The method of creation of mathematical models is developed for an assessment of lever properties of movements of mechanical oscillatory systems.

The method of definition of dynamical reactions in mechanical oscillation systems with rigid body with two degrees of freedom is discussed. Understandings about possibilities of creature of structural analogy schemes in relations with systems of automatic feed-back control are used. Transformations of structural schemes for selection of chain of feed-back ties in accordance in examination of object are shown. Such ties represent the dynamical reactions which are looked. Compare analysis with using several approaches are made. Peculiarities of method of definition of dynamical reactions in contacts of rigid body with elastic elements of mechanical oscillation systems are shown.

The hypothesis of formation of vibration conditions of a working environment based on representation that process of formation of interaction of elements in systems with not holding connections is considered as the process consisting of several phases is offered. Those are: contact phases at which reaction of connection is positive; a phase of a transition state when reaction is equal to zero; a gap phase in which the contacting surfaces can make the independent movements. Research problems are focused on specification of theoretical ideas of dynamic interactions of a solid body with the vibrating surface on the basis of the developed mathematical models received at introduction of additional external forces and elastic connections. Dynamic interactions of elements are considered; analytical approaches in an assessment of opportunities of vibration technological processes with continuous tossing of a working environment are defined and developed. The generalized approach for problems of dynamic synthesis which basis is introduction of concept about the function of a gap allowing to prove creation of trajectories of movements of material particles according to the certain criteria reflecting properties of trajectories of the movement of material particles in interaction with the vibrating surface is offered. The method of creation of mathematical models of formation of vibration interactions taking into account the factors having technological value or criteria to which conditions of realization of the multiple modes, influence of additional forces and elastic connections belong is developed. Within the generalized approach to the solution of problems of dynamic interaction of the loose environment with the vibrating surface possibilities of use of function of a gap for an assessment and research of forms of the movement of material particles according to influence of a number of the factors reflecting parameters of a vibration field, condition of interactions with environment and features of formation of the periodic modes of tossing are considered. The theorem of conditions and opportunities of realization of the steady modes of interaction with the vibrating surface is proved. The analytical ratios defining conditions of realization of forms of processes of interaction of a loose working environment with details in technologies of vibration hardening are received. Results of approbation of recommendations about creation of technological processes in the annex to an industrial technological complex are proposed.