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A.N. Danilin, "Vibrations of Mechanical Systems with Energy Dissipation Hysteresis," Mech. Solids. 52 (3), 254-265 (2017)
Year 2017 Volume 52 Number 3 Pages 254-265
DOI 10.3103/S0025654417030037
Title Vibrations of Mechanical Systems with Energy Dissipation Hysteresis
Author(s) A.N. Danilin (Institute of Applied Mechanics of the Russian Academy of Sciences, Leningradskii pr. 7, Moscow, 125040 Russia; Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia, andanilin@yandex.ru)
Abstract A phenomenological approach which we refer to as kinematic is proposed to describe hysteresis; according to this approach, the force and kinematic parameters of a mechanical system are related by a first-order ordinary differential equation. The right-hand side is chosen in the class of functions ensuring the asymptotic approach of the solution to the curves of the enveloping (limit) hysteresis cycle of steady-state vibrations. The coefficients of the equation are identified by experimental data for the enveloping cycle. The proposed approach permits describing the hysteresis trajectory under the conditions of unsteady vibrations with an arbitrary starting point inside the region of the enveloping cycle. As an example, we consider the problem on forced vibrations of a pendulum-type damper of low-frequency vibrations.
Keywords unsteady vibrations, energy dissipation hysteresis, kinematic approach, enclosing cycle, parameter identification, low-frequency vibration damper
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Received 21 April 2015
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