Resonance-induced energy localization in a weakly dissipative nonlinear chain
1Space Research Institute, Russian Academy of Sciences, Moscow 117997, Russia.
Physical Review. E
|August 17, 2018
Summary
Weak dissipation in nonlinear oscillator chains prevents large-amplitude resonance. Instead, it causes localized large-amplitude oscillations near the excitation point and energy escape for distant oscillators.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Mechanical vibrations
Background:
- Coupled nonlinear oscillators exhibit complex dynamics, including resonance phenomena.
- Weak dissipation can significantly alter the behavior of strongly nonlinear systems.
- Understanding energy localization is crucial for designing robust mechanical systems.
Purpose of the Study:
- Investigate resonance and resonance-induced localization in a dissipative nonlinear oscillator chain.
- Analyze the role of weak dissipation in controlling large-amplitude resonance.
- Determine conditions for energy localization and its distribution within the chain.
Main Methods:
- Analytical derivation of conditions for resonance and energy localization.
- Numerical simulations of the weakly dissipative nonlinear oscillator chain.
- Study of 1:1 (fundamental) resonance under harmonic excitation.
Main Results:
- Weak dissipation prevents large-amplitude resonance in strongly nonlinear chains.
- Resonance-induced localization leads to large-amplitude oscillations near the actuator.
- Distant oscillators escape resonance, with energy equipartition among them.
- Maximal energy concentration occurs on the excited oscillator.
Conclusions:
- Weak dissipation is a critical factor in controlling resonance and energy flow in nonlinear chains.
- Resonance-induced localization offers a mechanism for targeted energy dissipation.
- Analytical and numerical results demonstrate good agreement, validating the findings.
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