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Second-harmonic generation for dispersive elastic waves in a discrete granular chain.
V J Sánchez-Morcillo1, I Pérez-Arjona, V Romero-García
1Instituto de Investigación para la Gestión Integrada de las Zonas Costeras, Universidad Politécnica de Valencia, Carretera Natzaret-Oliva s/n, 46730 Grao de Gandia, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
Summary
Nonlinear waves in granular chains exhibit complex behavior. The study reveals how second harmonics influence wave propagation, leading to energy transfer or dissipation.
Area of Science:
- Condensed matter physics
- Nonlinear dynamics
- Wave propagation
Background:
- Granular chains exhibit unique wave propagation phenomena.
- Nonlinear lattice models like the Fermi-Pasta-Ulam (FPU) model are crucial for understanding these dynamics.
- Harmonic excitation can drive complex wave behaviors.
Purpose of the Study:
- To investigate nonlinear compressional wave propagation in a 1D granular chain.
- To analyze the influence of second harmonics on fundamental wave characteristics.
- To derive analytical expressions for wave amplitudes.
Main Methods:
- Utilized a one-dimensional granular chain model with quadratic nonlinearity (α-FPU model).
- Employed a successive approximations method for analytical solutions.
- Studied harmonic excitation at one end of the chain.
Main Results:
- Derived analytical expressions for static displacement and harmonic amplitudes.
- Demonstrated that both propagating and evanescent second harmonics affect wave propagation.
- Observed periodic energy transfer between first and second harmonics in the propagating regime.
Conclusions:
- Second harmonic behavior (propagating vs. evanescent) dictates nonlinear wave characteristics.
- Dispersion-induced energy transfer between harmonics is a key feature.
- The evanescent nature of the second harmonic suppresses this energy transfer.
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