A MATHEMATICAL MODEL FOR INVESTIGATION OF NONLINEAR WAVE PROCESSES IN A 2D GRANULAR MEDIUM CONSISTING OF SPHERICAL PARTICLES

V. I. Erofeev; I. S. Pavlov; N. V. Leontiev

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A MATHEMATICAL MODEL FOR INVESTIGATION OF NONLINEAR WAVE PROCESSES IN A 2D GRANULAR MEDIUM CONSISTING OF SPHERICAL PARTICLES

机译：球形颗粒二维颗粒介质中非线性波过程研究的数学模型

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摘要

A two-dimensional model of a crystalline (granular) medium, representing a square lattice consisting of elastically interacting spherical particles with three translational and three rotational degrees of freedom, is discussed. Nonlinear differential equations, describing the propagation and interaction of various types of waves in such medium, are derived. An analytical dependence of the coefficients of these equations on the microstructure parameters is found. When only the motion of the particles in the lattice plane is considered, the rotational degree of freedom of particles in the region of low frequencies can be ignored, and the obtained system degenerates into a two-mode system. It is shown that in a one-dimensional case the latter model allows a soliton solution on sheer deformation under the conditions of longitudinal static deformation.

机译：讨论了晶体（颗粒）介质的二维模型，该模型表示由具有三个平移和三个旋转自由度的弹性相互作用的球形粒子组成的正方形晶格。推导了描述这些类型的波在这种介质中的传播和相互作用的非线性微分方程。发现这些方程的系数对微观结构参数的解析依赖性。当仅考虑粒子在晶格平面中的运动时，可以忽略低频区域中粒子的旋转自由度，并且所获得的系统退化为双模系统。结果表明，在一维情况下，后一种模型允许在纵向静态变形条件下进行纯粹变形的孤子解。

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来源
《Composites: mechanics, computations, applications》 |2013年第3期|239-255|共17页
作者
V. I. Erofeev; I. S. Pavlov; N. V. Leontiev;
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作者单位

Mechanical Engineering Research Institute of the Russian Academy of Sciences,Nizhny Novgorod, Russia;

Mechanical Engineering Research Institute of the Russian Academy of Sciences,Nizhny Novgorod, Russia;

Mechanical Engineering Research Institute of the Russian Academy of Sciences,Nizhny Novgorod, Russia;

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正文语种 eng
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granular medium; structural modeling; microstructure parameters; soli-ton solution;

机译：颗粒状介质结构建模;微观结构参数溶液;

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A MATHEMATICAL MODEL FOR INVESTIGATION OF NONLINEAR WAVE PROCESSES IN A 2D GRANULAR MEDIUM CONSISTING OF SPHERICAL PARTICLES

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