Slidenko V.
Candidate of Technical Sciences, Associate professor, National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
Slidenko A.
Candidate of Physical and Mathematical Sciences, Associate professor, Voronezh
State Agricultural University, Voronezh, Russia
THE MODELING OF OSCILLATION SUPPRESSION
AT HYSTERESIS DAMPING
Introduction. The determining problem of the rational parameters of impulse
technical systems is to study the possibility of using analytical and numerical methods
for searching the solutions of initial-value problems with nonlinear stiffness and
viscosity characteristics of the hysteresis type. In the majority of impact actuators of
machines - hydraulic hammers, their feeders, connections of structural elements, the
stiffness and dissipation characteristics are more often nonlinear [1; 2; 3].
Characteristics which display damping properties can be both continuous and
discontinuous functions from displacement or speed [4; 5]. Damping properties are
more effective on conditions of hysteresis processes. In this case, the damping ability
can be estimated by the area of the hysteresis loop, and the damping properties are
determined by elastic constants and can be shown, for example, at strains that are much
less than the limit liquidity of the metal [6].
The problem of mechanical oscillation suppression of technical system elements
of rod type was studied in the following works [7-12]. The urgency of this problem is
especially evident in impact loads [13]. In this work [5], the use of a structural element
that provides a non-linear characteristic of resistance at impact loads is considered. The
efficiency of oscillation suppression with the help of such an element is experimentally
shown. The mathematical modeling of this process is important to prove the effective
oscillation suppression.
The model of oscillation suppression of tool-rod during impact load with the use
of an element with a nonlinear power characteristic is considered. The nonlinearity of
the power characteristic involves the dependence of the resistant force on the
displacement and the motion direction. The dependence of the resistant force on the
displacement and the motion direction was obtained experimentally and it was
approximated by a piecewise linear function of two variables. For controlling the
validity of the results, we consider a simplified single-mass sampled-data system with
a nonlinear element and an analytical solution is found for it. This solution is compared
with the numerical calculation obtained by the Runge-Kutta method using the
integrated functions of Mathcad system [14]. The initial-boundary value problem with
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