Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure

A. V. Porubov; I. E. Berinskii

doi:https://doi.org/10.1177/1081286515577040

Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure

Research output: Contribution to journal › Article › peer-review

Abstract

An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.

Original language	English
Pages (from-to)	94-103
Number of pages	10
Journal	Mathematics and Mechanics of Solids
Volume	21
Issue number	1
DOIs	https://doi.org/10.1177/1081286515577040
State	Published - Jan 2016
Externally published	Yes

Keywords

Nonlinear hexagonal lattice
asymptotic solution
continuum limit
nonlinear differential equation

All Science Journal Classification (ASJC) codes

Mechanics of Materials
General Materials Science
General Mathematics

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abstract = "An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.",

keywords = "Nonlinear hexagonal lattice, asymptotic solution, continuum limit, nonlinear differential equation",

author = "Porubov, {A. V.} and Berinskii, {I. E.}",

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year = "2016",

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doi = "https://doi.org/10.1177/1081286515577040",

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AU - Porubov, A. V.

AU - Berinskii, I. E.

PY - 2016/1

Y1 - 2016/1

N2 - An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.

AB - An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.

KW - Nonlinear hexagonal lattice

KW - asymptotic solution

KW - continuum limit

KW - nonlinear differential equation

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U2 - https://doi.org/10.1177/1081286515577040

DO - https://doi.org/10.1177/1081286515577040

M3 - مقالة

SN - 1081-2865

VL - 21

SP - 94

EP - 103

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

IS - 1

ER -

Two-dimensional nonlinear shear waves in materials having hexagonal lattice structure

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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