• Corpus ID: 195766825

# Passage through resonance for a system with time-varying parameters possessing a single trapped mode

@article{Shishkina2019PassageTR,
title={Passage through resonance for a system with time-varying parameters possessing a single trapped mode},
author={Ekaterina V. Shishkina and S. N. Gavrilov and Yulia A. Mochalova},
journal={arXiv: Classical Physics},
year={2019}
}
• Published 28 June 2019
• Physics
• arXiv: Classical Physics
We consider a forced oscillations of an infinite-length mechanical system, with time-varying parameters, possessing a single trapped mode characterized by frequency $\Omega_0(\epsilon t)$. The system is a string, lying on the Winkler foundation, and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. The discrete oscillator is subjected to harmonic external force with constant frequency $\hat\Omega$. In the case of the passage through the resonance, we obtain the…

## References

SHOWING 1-10 OF 26 REFERENCES
Evolution of a trapped mode of oscillation in a string on the Winkler foundation with point inhomogeneity
• Engineering
2017 Days on Diffraction (DD)
• 2017
We consider a mechanical system with mixed spectrum of natural oscillations. This is an infinite string on the Winkler elastic foundation with point inhomogeneity (the spring with negative
An Infinite-Length System Possessing a Unique Trapped Mode Versus a Single Degree of Freedom System: A Comparative Study in the Case of Time-Varying Parameters
• Engineering
Dynamical Processes in Generalized Continua and Structures
• 2019
We compare large time behavior of an infinite system, with time-varying parameters, possessing a unique trapped mode (characterized by frequency $$\varOmega _0(\varepsilon \tau )$$), with the
Non-stationary localized oscillations of an infinite string, with time-varying tension, lying on the Winkler foundation with a point elastic inhomogeneity
• Engineering
Nonlinear Dynamics
• 2019
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative
Passage Through Resonance for a One-Dimensional Oscillator with Slowly Varying Frequency
This paper concerns a model problem illustrating the techniques needed to handle passage through resonance for oscillatory systems with slowly varying frequencies. The model consists of a linear
Resonance vibrations of elastic waveguides with inertial inclusions
• Physics
• 2000
The problem of resonance oscillations of inertial inclusions in contact with elastic waveguides has triggered a number of theoretical investigations. It was shown [1–3] that related phenomena may be
On the Problem of Sustained Resonance
• Physics
• 1978
An investigation of a model for reentry roll resonance reported in an earlier paper by the second author is continued. First, numerical integration is employed to verify the main results of the
Semi-Resonant Interactions and Frequency Dividers
• Physics
• 1973
A theory describing the behavior of a system as it evolves slowly through internal nonlinear resonances is presented. The energy sharing process is seen to be quite complex as it depends crucially on