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


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.


Launch Vehicle Ukrainian National Academy Nonlinear Feedback String Generator Ballistic Missile 
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© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKievUkraine

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