Nonlinear Acoustic Waves in Solids with Dislocations

Propagation of a plane longitudinal acoustic wave in a solid with dislocations is theoretically studied. The effect of dislocations on the phase velocity dispersion and the character and degree of wave damping is analyzed. The following results are obtained. The phase velocity exhibits infinite growth at zero frequency and asymptotically approaches the tabulated value for the longitudinal wave velocity in solids as the frequency tends to infinity. The frequency dependence of the wave damping coefficient has a peak whose position depends on the characteristics of the solid. The results are compared with experimental data for the dislocation relaxation process in lead and are found to be in good agreement with these.The influence of the dislocation structure on the character of the dependencies obtained for wave damping and phase velocity dispersion is analyzed. The results are compared with experimental data for the dislocation damping during plastic deformation and cycling loading of polycrystalline copper and aluminum.We derive the dynamic equations of solid media with dislocations containing geometrical and physical nonlinearity. The evolution of nonlinear acoustical waves under the influence of a dislocation field is studied. The development of modulation instability quasiharmonic longitudinal waves is shown to be possible.