The nonlinear viscoelastic cosserat model for the wave propagation with generation of subharmonics

Cosserat model is developed in nonlinear form to describe the appearance of lower frequencies in seismic waves spectra[ As in the Ericksen theory of liquid crystals\ elastic and viscous rheological elements are combined to get sensible results[ The translational degrees of freedom are described by linear elasticity but the rotational kinematically independent motion is governed by the nonlinear elastic potential and linear viscosity[ The dynamics of linear perturbations show that the longitudinal translations and rotations both decouple completely from other motions[ These rotations represent local oscillations due to the existence of the potential and they do not propagate[ However\ the linear transverse translations and microrotations are coupled[ It is shown that they describe seismic and acoustic waves[ In the nonlinear case these motions demonstrate some new interesting phenomena[ For instanceif the propagation of the harmonic elastic wave is considered the microrotations behave like nonlinear oscillators excited by the external harmonic force[ Thus the system produces the same e}ects as those obtained recently for the Du.ng type equation with the help of the theory of attractors[ This means that the initial harmonic wave generates secondary waves with lower frequenc! ies[ These secondary frequencies are usually commensurable with the initial ones[ Numerical results show that the phenomenon still takes place if the initial wave consists of continuously distributed harmonics[ The generation of lower frequencies in granular media has been observed and reported but the theoretical explanation was lacking since it was thought conventionally that weak nonlinearities were able to produce higher frequencies only[ 0887 Elsevier Science Ltd[ All rights reserved[