A nonlinear mathematical model has been worked out for a two-dimensional granular medium that represents a square lattice consisting of elastically interacting round particles with longitudinal, transverse and rotational degrees of freedom. In the low-frequency range, the rotational degree of freedom can be neglected, and the obtained three-mode model reduces to a two-mode one. Numerical estimates of nonlinearity coefficients have been given for both models by obtained analytical dependences of these coefficients on the microstructure parameters.
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