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LIMIT CYCLES IN THE DYNAMICS OF AN ELASTICALLY MOUNTED AERODYNAMIC PENDULUM

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Abstract

The dynamics of a elastically mounted single-link aerodynamic is considered. The unsteady aerodynamic action is modeled using an attached oscillator. It is assumed that the stiffness of the mounting spring contains cubic term, in addition to the linear one. Equilibrium positions of the pendulum and their stability are investigated. It is shown, in particular, that at certain values of the parameters of the system, the “weather vane” equilibrium position becomes unstable, and an attracting limit cycle arises. Approximate formulas for the frequency and amplitude of this cycle are obtained. It is shown that, in a wide range of parameter values, its frequency practically does not depend on the coefficient of stiffness of the fastening spring and on the moment of inertia of the pendulum. The amplitude of the cycle increases with an increase in the moment of inertia and decreases with an increase in the stiffness coefficient.

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Funding

The study was carried out with the support of the Interdisciplinary Scientific and Educational School of Moscow University “Fundamental and Applied Space Research”

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Authors and Affiliations

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

    Yu. D. Selyutskiy

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  1. Yu. D. Selyutskiy
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Correspondence to Yu. D. Selyutskiy.

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Translated by Borimova A.A.

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Selyutskiy, Y.D. LIMIT CYCLES IN THE DYNAMICS OF AN ELASTICALLY MOUNTED AERODYNAMIC PENDULUM. Mech. Solids 57, 111–120 (2022). https://doi.org/10.3103/S0025654422010137

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