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Isolated frequencies at which nonlinear materials behave linearly.
Matthew D Fronk1, Michael J Leamy1
1School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Physical Review. E
|December 25, 2019
Summary
Specific frequencies in nonlinear lattices can prevent harmonic generation, enabling linear behavior. This discovery enhances signal-to-noise ratios in nonlinear devices like sensors and communication systems.
Area of Science:
- Physics
- Nonlinear Dynamics
- Materials Science
Background:
- Weakly nonlinear lattices typically generate higher harmonics, complicating signal processing.
- Understanding the conditions for linear behavior in nonlinear systems is crucial for device applications.
Purpose of the Study:
- To identify specific frequencies in weakly nonlinear lattices where higher harmonic generation is suppressed.
- To demonstrate that plane-wave solutions at these frequencies exhibit remarkably small spatiotemporal harmonic production.
Main Methods:
- Utilized multiple scales analysis to derive plane-wave solutions.
- Investigated monatomic and diatomic chains with quadratic and cubic nonlinearities.
- Employed direct numerical integration of equations of motion to validate findings.
Main Results:
- Identified specific frequencies that avoid higher harmonic generation in nonlinear lattices.
- Confirmed that plane waves at these frequencies maintain a single frequency and wave number.
- Numerical simulations verified negligible higher harmonic production for finite amplitude waves.
Conclusions:
- Weakly nonlinear lattices can exhibit linear behavior at specific frequencies.
- These findings offer new operating frequency considerations for nonlinear communications, sensors, and transducers.
- Enhanced signal-to-noise ratios are achievable by exploiting these frequency-selective linear behaviors.
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