Nonlinear normal modes of multi-walled nanoshells with consideration of surface effect and nonlocal elasticity

Avramov, K.

doi:10.1016/j.ijnonlinmec.2023.104622

Cited by 5 publications

(1 citation statement)

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“…Nonlinear elasticity wave equations are generated by the elastic wave propagation in inelastic material. These equations provide a specific explanation of material response under large deformations and elucidate complex nonlinear phenomena observed in various engineering applications, including structural engineering, aerospace engineering, and geological engineering [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions of a Hyperelastic Dispersive Equation

Jiang,

Tian,

2024

Mathematics

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This paper explores solitary wave solutions arising in the deformations of a hyperelastic compressible plate. Explicit traveling wave solution expressions with various parameters for the hyperelastic compressible plate are obtained and visualized. To analyze the perturbed equation, we employ geometric singular perturbation theory, Melnikov methods, and invariant manifold theory. The solitary wave solutions of the hyperelastic compressible plate do not persist under small perturbations for wave speed c>−βk2. Further exploration of nonlinear models that accurately depict the persistence of solitary wave solution on the significant physical processes under the K-S perturbation is recommended.

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Section: Introductionmentioning

confidence: 99%