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Nonlinear Oscillations

, Volume 11, Issue 2, pp 177–199 | Cite as

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

  • D. G. Korenevskii
  • A. M. Pil’kevich
Article
  • 23 Downloads

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.

Keywords

Launch Vehicle Ukrainian National Academy Nonlinear Feedback String Generator Ballistic Missile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKievUkraine

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