A nonlinear granular medium with particle rotation: A one-dimensional model

Equations of nonlinear acoustics are derived from the micromechanical repre sentation of a granular medium as a system of elastically interacting parti cles possessing translational and rotational degrees of freedom. The struct ure of the equations is, invariant with respect to the shape and size of th e particles. The changes, in the latter affect only the coefficients in the equations. The inclusion of microrotations and moment interactions of part icles leads to the formation of a new type of waves in the medium-microrota tional waves. Their dispersion properties are similar to those of spin wave s propagating in a magnetoelastic medium. In the low-frequency approximatio n, the microrotational waves disappear, and the equation describing the tra nsverse waves acquires a term with quadratic nonlinearity. The latter provi des an explanation for the generation of the second shear harmonic that is observed in real solids contrary to the predictions of the nonlinear theory of elasticity, which prohibits such phenomena. (C) 2001 MAIK "Nauka/Interp eriodica".