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Energy localization in weakly dissipative resonant chains
1Space Research Institute, Russian Academy of Sciences, Moscow 117997, Russia.
Physical Review. E
|September 15, 2016
Summary
Weak dissipation in nonlinear resonance arrays can prevent full chain resonance. Instead, energy localizes, causing large oscillations near the actuator and small ones further away.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Oscillator systems
Background:
- Energy localization in nonlinear oscillator arrays is a known phenomenon.
- Previous research focused on nonlinearity and discreteness.
- The role of dissipation in energy localization was less explored.
Purpose of the Study:
- Investigate energy localization in nonlinear resonance arrays with dissipation.
- Examine the effect of weak dissipation on resonance in oscillator chains.
- Determine conditions for resonance emergence and energy localization.
Main Methods:
- Modeling a finite Klein-Gordon chain with dissipation.
- Applying harmonic excitation at one edge.
- Analytical derivation of resonance and localization conditions.
- Numerical simulations for validation.
Main Results:
- Weak dissipation prevents resonance in the entire chain.
- Energy localizes, creating distinct oscillation amplitude zones.
- Large-amplitude resonance occurs near the actuator.
- Small-amplitude oscillations are observed in the distant chain parts.
Conclusions:
- Dissipation is a critical factor in energy localization in nonlinear resonance arrays.
- The derived conditions accurately predict resonance and localization.
- Analytical and numerical results show strong agreement.
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