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Method for Generating Asynchronous Self-Sustained Oscillations of a Mechanical System with Two Degrees of Freedom

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Abstract

An autonomous nonconservative mechanical system with two degrees of freedom is studied. The system is subject to a feedback control with two control impact gain factors. It is required to select the values of these factors in such a way as to ensure existence of asynchronous self-sustained oscillations with prescribed properties. An iterative method is proposed to search for the corresponding values of control impact gain factors. This approach is based on constructing auxiliary second-order systems and generating limit cycles in these systems. The algorithm that is used for this purpose represents a modification of the Andronov–Pontryagin method, but does not require the presence of a small parameter in the system. The efficiency of this approach is illustrated on a problem of generating asynchronous self-sustained oscillations/rotations in a model of an aerodynamic pendulum. The applicability conditions of the algorithm and the possible modifications are discussed.

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Funding

The study is supported by the Interdisciplinary Scientific and Educational School of Moscow University “Mathematical Methods of Complex Systems’ Analysis.”

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Authors and Affiliations

  1. Institute of Mechanics, Lomonosov Moscow State University, 119192, Moscow, Russia

    L. A. Klimina

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  1. L. A. Klimina
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Correspondence to L. A. Klimina.

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Translated by E. Oborin

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Klimina, L.A. Method for Generating Asynchronous Self-Sustained Oscillations of a Mechanical System with Two Degrees of Freedom. Mech. Solids 56, 1167–1180 (2021). https://doi.org/10.3103/S0025654421070141

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