Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures

HOU Xiu-hui; DENG Zi-chen; ZHOU Jia-xi

doi:10.3879/j.issn.1000-0887.2010.11.004

Volume 31 Issue 11

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HOU Xiu-hui, DENG Zi-chen, ZHOU Jia-xi. Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1297-1307. doi: 10.3879/j.issn.1000-0887.2010.11.004

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Symplectic Analysis for Wave Propagation in One-Dimensional Nonlinear Periodic Structures

doi: 10.3879/j.issn.1000-0887.2010.11.004

1.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-10-01
Publish Date: 2010-11-15

Abstract

Abstract

The wave propagation problem in nonlinear periodic mass-spring structure chain was analyzed using the symplectic mathematical method. Firstly the energy method was applied to construct the dynamical equation and then the nonlinear dynamical equation was linearized using the small parameter perturbation method. The eigen-solutions of the symplectic matrix were applied to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain,arising from the nonlinear spring stiffness effect,has profound effects on the overall transmission of the chain. The wave propagation characteristics are not only altered due to the nonlinearity but also related with the incident wave intensity, which is a genuine nonlinear effect that is not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to a closing of the transmitting gaps. Comparison with the normal recursive approach demonstrates the effectiveness and superiority of the symplectic method in wave propagation problem for nonlinear periodic structures.
- symplectic mathematical method,
- nonlinear periodic structure,
- elastic wave propagation

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References

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