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Minimizing resonant oscillations in a system with variable structure

DOI 10.18127/j19997493-201804-08

Keywords:

Yu.N. Pavlov – Dr.Sc.(Eng.), Professor, Department «Information Systems and Telecommunications», Bauman Moscow State Technical University
E-mail: pavlov@bmstu.ru
V.V. Nedashkovsky – Ph.D.(Eng.), Associate Professor, Department «Information Systems and Telecommunications», Bauman Moscow State Technical University
E-mail: vmniu3@bmstu.ru
V.I. Oganov – Associate Professor, Department «Information Systems and Telecommunications», Bauman Moscow State Technical University
E-mail: oganov@bmstu.ru
E.A. Tikhomirova – Associate Professor, Department «Information Systems and Telecommunications», Bauman Moscow State Technical University
E-mail: elizarti@bmstu.ru


The article deals with the problem of minimizing resonant vibrations in mechanical structures by means of dynamic quencher of forced oscillations.
In the used dynamic quenchers of oscillations with viscous friction, damping qualities are significantly reduced, since the properties of the viscous liquid in the composition of these quencher of oscillations are very unstable when the temperature changes in the range from −40°C to +40°C. Dry friction is devoid of this drawback and therefore it can be assumed that in this case the quencher of oscillations will be effective throughout the temperature range. The goal is to search a variant of minimizing resonant oscillations in a system with a variable structure.
The article describes the option of minimizing resonant oscillations in a system with a dynamic quencher of oscillations consisting of two bodies: the main body, the forced oscillations of which must be extinguished, and the quencher of oscillations. The energy introduced by the perturbing periodic force is dissipated by the damper of dry friction with the relative motion of the bodies. However, it is known that the dry friction damper damping oscillations near the resonant frequencies does not work at the resonant frequencies and the amplitude-frequency response at the resonant frequency has a gap.
The article proposes a method for solving the problem of resonances in a system with a damper of dry friction, based on the following fact of change of the system structure near the resonant frequencies. As long as the inertial force of the quencher of oscillations does not exceed the value of the dry friction force, the system of two bodies (the main body and the quencher of oscillations behaves as a system of one solid body, including a rigidly coupled main body with the quencher of oscillations. Uncoupling of the main body and of the quencher of oscillations at near-resonant frequencies occurs at the moment when the inertial force of the quencher of oscillations begins to exceed the force of dry friction. After uncoupling, the system behaves as a system of two bodies of the main body and a damper of dry friction connected by a rigid spring and a dry friction damper. In other words, at the moment of uncoupling there is a change of the system structure.
In the algorithm it is proposed to use the method of harmonic linearization. The nonlinearity of the «dry friction» type is suggested to be approximated by viscous friction with the corresponding coefficient of harmonic linearization. In the article the expressions for calculating the spring stiffness of the quencher of oscillations and the value dry friction of the damper to minimize the resonant oscillations of the main body are obtained. The resulting expressions can be used as ready-made calculation formulas.

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