Eliseev

 The authors propose a technique of creating various mathematical models of mechanical oscillatory systems with two degrees of freedom with elastic supports and a rigid body for protection against vibrations. The problem is solved by selection of corresponding motion coordinates. It is supposed that after realization of a system of joints between the rigid body and the base of the system, choice of corresponding coordinates is made. Those coordinates describe relative movement between two selected points. After transformation of a mathematical model and the setting coordinate of relative movement equal to zero, the system loses one degree of freedom. The mathematical model of the system is simplified; it allows one to estimate dynamical properties of the system from the required point of view. The proposed method also allows one to search for and estimate new constructional and technical solutions in the field of protection against vibration and vibration isolation of technical systems.

The authors propose a technology for creating mathematical models of mechanical oscillatory systems with a chain structure and several degrees of freedom. Various descriptions of movement in different coordinates are considered. Some coordinates characterize relative motion. Nulling of such coordinates results in combining corresponding mass-inertia elements; hence, the system on the whole reduces the number of degrees of freedom by one. Generalization allowing to set several coordinates equal to zero simultaneously is also considered. Some examples are provided.

The authors consider a mechanical system that has an object of protection in the form of a solid body on two elastic supports. The object of protection has a mass and a moment of inertia and can oscillate around the center of gravity. The dynamic lever vibration dampener has a lever construction and a support point on the object as a rotary joint. Movement of the hinge or choosing a seat for the dampener can significantly change the properties of the system as a whole. Features of the dampener include expression of dynamic properties which depend on the choice of the generalized coordinate system. The authors propose a method of constructing mathematical models and evaluating dynamic properties. They also give results of numerical experiments.

Possibilities of creation of structural schemes of mechanical oscillation systems are considered in this article. The authors propose an integration method which combines possibilities of using principles of electromechanical analogies (mechanical chains) and rules of structure transformations with feedback coupling. A methodological base for evaluating dynamic properties of vibration protection systems with electromechanical couplings was proposed.

The authors consider questions of creating mathematical models of mechanical systems with couplings. Usually the couplings are simple rotational kinematical ties. The authors propose a method of model creation – this method consists of implementation of a certain sequence of actions based on selection of points of possible coupling of two bodies and a system of corresponding coordinates. If the elements of the planned coupling are identified as points of possible contact and are interconnected with an elastic or dissipative coupling, the difference between the coordinates of two selected points defines the relative coordinate. This coordinate can be removed out of the coefficient matrix of the system of motion equations with an appropriate column and line delineation. Coupling introduction is accompanied with a decrease in the number of degrees of freedom. Several examples, including one for two couplings, are considered in the article.

The authors propose a methodical foundation of estimation and research of origination of dynamical damping of oscillations for tasks of vibration protection of machines and equipment. The novelty of the approach consists of using a new class of mathematical models for mechanical systems; these models represent structural schemes as the equivalent of dynamic systems of automatic control. The authors consider questions of scientific substantiation of structural transformations of mathematical models with selection of feedback couplings, inherent in elastic oscillation systems. A dynamical oscillation damper in the vibration protection system within the framework of the developing concept was considered as feedback of a certain type. The authors propose a technology of detection of dynamical damping of frequencies in systems with several degrees of freedom. The authors show possibilities of improvement of the “dynamical damping of oscillations” concept the physical meaning of which essentially depends on the choice of synthesis coordinates. The authors propose a synthesis method for building vibration protection systems with dynamical absorbers of oscillations. The numeric simulation and laboratory experiment results are included in the article.

Dynamical interactions in mechanical oscillation system are considered, in which object of protection is connected with additional mass through kinematical couple. Is shown that introduction of additional ties if there is absorber of oscillation may change frequencies properties of the system significantly.

Methodical bases for building of transport mathematical models  vibroprotection systems are suggested. Considered systems have lever mechanisms and additional ties, which can be realized through using of elementary typical links of widen collection.

Questions of influence of position of dynamical absorber on properties of object with two degrees of freedom are considered. Building of effective system of defense from vibration and getting of additional regimes of dynamical absorbtion with coupling are offered.