# resonance

## Asymptotic method in investigation of complex nonlinear oscillations of elastic bodies

The main provisions of the methodology of the study of complex oscillations of elastic bodies are outlined.

## Justification of the rational length of the long-acting working body of the vibration transporting device

The article deduces an analytical dependence that establishes for a long vibration vehicle a rational length of a working body, as a body with a distributed mass, since it is impossible to match its own frequency of oscillations with the forced.

## Identification of ways to further improve of highly effective interresonance oscillatory systems

The article substantiates the possibility of further improvement of highly effective interreonance oscillatory systems. To do this, it is proposed to apply a discrete-continuum oscillation system in which a third ultra-light mass is used as a body with distributed parameters (ultra-light weight).

## MODELLING THE PROCESS OF DRESSING THE LAPS OF VIBRATORY FINISHING MACHINE

The purpose of the paper. Substantiation of structure (design), parameters and operation modes of the improved vibratory finishing machine. Analysis of dynamical processes which occur during “lap over lap” dressing. Investigation methodology. Mathematical model of motion of the mechanical system of vibratory finishing machine was developed on the basis of Lagrange differential equations of the second order. For the purpose of describing friction between the working surfaces of the laps, the Coulomb friction model was used.

## Kolyvannia kiltsevoho elektromahnitnoho vibrokavitatora rezonansnoi dii [Oscillations of the ring’s electromagnetic resonance vibratory cavitator at the resonance mode]

Worked out calculation chart on the basis of equalizations of Lagrange the second family the system of linear differentialequalizations in a matrix form, that describe a shakeprocess in circular electromagnetic cavitator of resonantaction, is got, and it is got solution of matrix equalization in a complex form.

## Comparative analysis of the resonant vibro-impact two and three-mass structure systems with linear friction

The optimization model based on the criteria of energy efficiency of vibration systems is considered. This criterion is presented as the ratio of maximum of the working mass acceleration to consumption power of system. Optimization task is added of constraints that determine the technological aspects of vibrational resonant type - the width of the resonance zone, coefficient asymmetry of acceleration, maximum acceleration of the working mass. Searching of stiffness of asymmetric piecewise linear elastic properties at the basic of synthesis is entrusted.

## Justification of parameters of the vibratory hopper feeder with an electromagnetic drive

In the article is an example of a vibrating hopper feeder full methodology described his design with the withdrawal of the main analytical dependencies that set the parameters of the system

## Оптимізація режимів віброрезонансної кавітаційної обробки рідин

The method of vibration of cavitation treatment of substances of liquids and device is described for determination of frequencies of resonances of own vibrations of present in the processed liquids embryos of cavitation. It is proved that optimum are the modes which frequencies of vibrations of cavitation are multiple frequencies of own vibrations of embryos of cavitation at.

## Зміна характеристик робочих поверхонь деталей при звуковій вібраційній обробці в пружному середовищі

In the article the considered change of basic tribological descriptions of superficial layer of workings surfaces of pair of friction is at their voice oscillation treatment in a resilient environment. The technological parameters of process of treatment and of principle chart of setting are analysed. The results of conducted experimental treatment of details are rotined.

## Estimation parameters unsteady fluctuations crane systems with one degree of freedom of movement in the vibrovyprobuvan of mechatronic controlsystems

When testing the crane systems via the wobble frequency method they undergo the consequent influence of vibrations at all frequencies of the set range. The choice of modes of the crane systems’ accelerated tests with respect to sinusoidal vibration influence at the changing transmitter frequency requires the definition of the dynamic amplitude frequency characteristics (AFC) of items of the cranes’ mechatronic supervision systems (MSS).