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Nonlinear dynamics of coupled transverse-rotational waves in granular chains
Qicheng Zhang1,2,3, Olga Umnova4, Rodolfo Venegas5
1Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China.
Physical Review. E
|January 23, 2020
Summary
This study explores nonlinear wave dynamics in granular chains. Nonlinear interactions generate new frequencies, enabling efficient energy transfer in systems with substrates, unlike those without.
Area of Science:
- Nonlinear Dynamics
- Condensed Matter Physics
- Wave Propagation
Background:
- Granular chains exhibit complex wave behaviors.
- Nonlinear interactions are crucial for understanding energy transfer.
Purpose of the Study:
- To theoretically investigate nonlinear dynamics of coupled waves in 1D granular chains.
- To analyze the influence of a substrate on wave interactions and energy transfer.
Main Methods:
- Utilized the multiple time scale method.
- Derived nonlinear dispersion relations for infinite chains.
- Obtained wave solutions for semi-infinite systems.
Main Results:
- Quadratic nonlinearity generates sum and difference frequency components from coupled transverse-rotational and longitudinal waves.
- Chains without substrates show low-amplitude frequency components and beating oscillations.
- Chains with substrates exhibit two types of nonlinear resonances, leading to efficient energy transfer.
Conclusions:
- Nonlinear resonances in substrate-supported granular chains facilitate efficient energy transfer between waves.
- Findings suggest potential applications in acoustic devices for energy transfer and rectification.
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