Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

Liu, Zhiguo; Wang, Yue‐Sheng; Huang, Guoliang

doi:10.1103/physreve.99.062904

Cited by 11 publications

(17 citation statements)

References 77 publications

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“…It is indeed not difficult to verify that the derivations of the solutions in Ref. [34] w.r.t the space coordinate x are the same as the bright solitary wave solutions ( 27)- (31). However, we found that the coefficient ij A in the present multiple-solitary wave solutions and those in Ref.…”

Section: ) the Bright Double-solitary Wave Solutionmentioning

confidence: 89%

“…(33) Theoretically, the solitary wave solutions obtained above and the asymptotic solutions constructed in Ref. [34] (see Eqs. ( 30)-( 33) therein) are different representations of the same physical phenomenon.…”

Section: ) the Bright Double-solitary Wave Solutionmentioning

confidence: 97%

“…(6) in Ref. [34]). However, only approximate analytical solutions of multiple-solitary waves were constructed without rigorous mathematical derivation.…”

Section: Introductionmentioning

confidence: 96%

“…In Ref. [34], we obtained the exact analytical single solitary wave solution from this continuous equation (Eq. (6) in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

Liu¹,

Zhang²,

Wang³

et al. 2021

Preprint

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In this paper, the governing equation in a pre-compressed one-dimensional granular crystal, which was previously discussed by Nesterenko [J. Appl. Mech. Phys. 24, 733 (1983)], is solved analytically. Multiple solitary wave solutions are obtained by using the homogeneous balance principle and Hirota’s bilinear method. We analyze the difference between the original system and the KdV system and examine the collision of solitary waves in some special parameters. The dynamic behavior and stability of the double solitary waves are also studied. We find that the opposite collision between single solitary waves may be stable and thus generate a stable double solitary wave. It is concluded that the collision is a special stable double solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively.

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Section: ) the Bright Double-solitary Wave Solutionmentioning

confidence: 89%

Section: ) the Bright Double-solitary Wave Solutionmentioning

confidence: 97%

See 2 more Smart Citations

Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

Liu¹,

Zhang²,

Wang³

et al. 2021

Preprint

Self Cite

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show abstract

“…Moreover, In Reference [14] the approximate bright and dark solitary wave solutions were obtained in the chain of elastic spheres.…”

Section: Introductionmentioning

confidence: 99%

The Exact Solitary Wave Solutions in Continuity Equation of the One-Dimensional Granular Crystals of Elastic Spheres

Liu¹,

Zhang²

2019

JAMP

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In this paper, we reduced the governing equation describing the one-dimensional granular crystals of elastic spheres to a continuous equation by small deformation and long wave approximation. Then, the G'/G-expansion method is applied to this continuous equation, and the exact solitary wave solutions with arbitrary parameters are obtained. Compared with other papers, the solutions obtained in this paper are more extensive and contains more parameters. The simultaneous existence of exact solitary wave solutions can help us study the propagation of shock waves in one-dimensional granular crystals of elastic spheres. At the same time, it has important theoretical significance in nondestructive testing with non-linear wave.

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Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

Wang

2021

Acta Mech. Solida Sin.

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In this work, the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied, in which the interface between different granular chains is considered. Due to the discontinuity of two periodic granular systems, the transmitted and reflected solitary waves are produced. The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves. According to the derivation and numerical simulation, we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain. Moreover, the influences of both the arrangement and prestress are discussed. It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress, which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials. This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

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Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities

Cited by 11 publications

References 77 publications

Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

The Exact Solitary Wave Solutions in Continuity Equation of the One-Dimensional Granular Crystals of Elastic Spheres

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

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