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On the dynamics of a string generator: Effect of delay in nonlinear feedback

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Nonlinear Oscillations

Abstract

We investigate the effect of delay in feedback on the oscillation characteristics (amplitude and frequency) of a string generator, which, as is well known, works in a self-induced oscillation mode and is a part of a string accelerometer (a device for measuring the acceleration of ballistic missiles, launch vehicles, and other moving objects). A mathematical model of the dynamics of a string generator is taken in the form of a quasilinear second-order hyperbolic equation with constant delay with respect to one of independent variables (time). For the analysis of the mathematical model, we use the one-frequency asymptotic Krylov-Bogolyubov-Mitropol'skii method (its first and second approximations) of nonlinear mechanics. We show that an increase in the delay in the nonlinear feedback amplifier results in a decrease in the frequency of self-induced oscillations, which transforms the string generator into a low-frequency device.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    D. G. Korenevskii & A. M. Pil’kevich

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  1. D. G. Korenevskii
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  2. A. M. Pil’kevich
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Correspondence to D. G. Korenevskii.

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__________

Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 168–190, April–June, 2008.

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Korenevskii, D.G., Pil’kevich, A.M. On the dynamics of a string generator: Effect of delay in nonlinear feedback. Nonlinear Oscill 11, 177–199 (2008). https://doi.org/10.1007/s11072-008-0023-7

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  • DOI: https://doi.org/10.1007/s11072-008-0023-7

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