# resonance

## Study of the dynamic process in a nonlinear mathematical model of the transverse oscillations of a moving beam under perturbed boundary conditions

The study of transverse oscillations of systems moving along their axis is a very difficult, but at the same time a very important task.  Mathematical models of nonlinear transverse oscillations of a beam moving along its axis are analyzed in this paper work, both for non-resonant and resonant cases.  The task becomes even more complicated if we additionally take into account the method of fastening the ends of the beam or the perturbation at its ends.  We have obtained dependencies that can be used in construction, transport, industry, mechanical engineering and other

## On the external and internal resonance phenomena of the elastic bodies with the complex oscillations

Complex nonlinear oscillations in the elastic bodies are studied using a priori information about the oscillations form and taking into account a refined mathematical model of the second (other) form of oscillations.  Application of existing methods or development of the new ones for the analysis of received non-autonomous boundary value problems is proposed.  The effectiveness of the practical implementation of the discussed methodology significantly increases in cases where the magnitude of the elastic body displacements due to the one form of oscillations is much higher than the other on

## Determination of parameters of vibro-impact machines taking into account their main characteristics

Aim. The purpose is to form a generalized performance indicator and analysis of resonant vibration machines, taking into account their main energy, dynamic and technological characteristics. Method. Three basic parameters the ratio of the maximum acceleration of the working mass to the power consumption, the coefficient of asymmetry of acceleration and the width of the resonance zone were used to evaluate the efficiency of vibration systems. These indicators are reduced to a dimensionless form in the next step.

## 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