# Mathematical Modelling of Dynamics of the Vibroprotective System Equipped with Roller Absorber

## Authors

• Дмитро Вікторович Легеза NTUU KPI, Ukraine

## Keywords:

Vibroprotective system, Isochronous roller absorber, Brachystochrone for a roller, Settled forced oscillations, Amplitude-frequency characteristic, Parameters of tuning of absorber

## Abstract

Using the methods of mathematical modeling to develop numeral-analytical approach for determination of equations of ACHKH of the nonlinear vibroprotective system with a new isochronous roller absorber in the first approaching and to define the optimum parameters of its tuning. For the conclusion of equations ACHKH the averaging method of W. Ritz, adapted to the probed task, was used. For the solution of nonlinear algebraic equations of ACHKH of the system the special programmatic complex was developed in a non-obvious form. For determination of optimum parameters of tuning of roller absorber, a numeral-graphic method is offered and a numeral experiment is conducted on determination of the indicated parameters. It is set on the basis of numeral experiment, that the own frequency of the optimum adjusted absorber in the nonlinear raising does not coincide with the own frequency of the optimum adjusted absorber in the linear raising. In addition, the maximal values of amplitudes of bearing body for linear and nonlinear tasks differ substantially: a rejection makes about 10 % (less than for a nonlinear task).  Main advantage of the offered roller absorber consists of that frequency of own oscillations of absorber does not depend on the relative rejections of its working body. Therefore even at the large relative rejections of working body of absorber originally adjusted his parameters remain stable, and oscillations – isochronous. It is determined that the offered absorber is effective enough: it is possible using it to decrease substantially the level of amplitudes of the forced oscillations of bearings bodies.

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