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ISSN Druckformat: 2152-2057
ISSN Online: 2152-2073
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A MATHEMATICAL MODEL FOR INVESTIGATION OF NONLINEAR WAVE PROCESSES IN A 2D GRANULAR MEDIUM CONSISTING OF SPHERICAL PARTICLES
ABSTRAKT
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.
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