Second-harmonic generation for dispersive elastic waves in a discrete granular chain

被引：47

作者：

Sanchez-Morcillo, V. J. ^{[1
]}

Perez-Arjona, I. ^{[1
]}

Romero-Garcia, V. ^{[1
]}

Tournat, V. ^{[2
]}

Gusev, V. E. ^{[3
]}

机构：

[1] Univ Politecn Valencia, Inst Invest Gest Integrada Zonas Costeras, Gandia 46730, Spain

[2] Univ Maine, LUNAM Univ, CNRS, LAUM UMR 6613, F-72085 Le Mans, France

[3] Univ Maine, LUNAM Univ, CNRS, IMMM UMR 6283, F-72085 Le Mans, France

来源：

PHYSICAL REVIEW E | 2013年 / 88卷 / 04期

关键词：

SOLITARY WAVES; TRANSMISSION; PROPAGATION; MODEL;

D O I：

10.1103/PhysRevE.88.043203

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The propagation of nonlinear compressional waves in a one-dimensional granular chain driven at one end by a harmonic excitation is studied. The chain is described by a Fermi-Pasta-Ulam (FPU) lattice model with quadratic nonlinearity (alpha-FPU model), valid for strong initial compression of the chain by an external static force. A successive approximations method is used to obtain the analytical expressions for the amplitudes of the static displacement field and of the fundamental and second harmonics propagating through the lattice. Both propagating and evanescent second harmonics are shown to influence the nonlinear propagation characteristics of the fundamental frequency. The propagating regime is characterized by a periodic energy transfer between first and second harmonics, resulting from dispersion, which disappears when the second harmonic becomes evanescent.

引用

页数：8

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