NONLINEAR-INTERACTIONS OF LONGITUDINAL AND HELICAL SHEAR-WAVES IN A SOLID BODY WITH A MICROSTRUCTURE

We studied the multiwave nonlinear resonance interactions of elastic w aves in a solid body with a microstructure. The study was carried out with a model of a medium with moment stresses (Le Roux continuum) gene ralized to account for geometrical and physical nonlinearities. A squa re-law nonlinearity was shown to cause the resonance interaction of th ree waves: a plane-polarized longitudinal shear wave and two shear wav es of circular polarization (helical waves). The frequencies and wave numbers of interacting waves were related by the conditions of phase s ynchronism and they satisfy the dispersion equations. The effect of sp litting instability was found to take place in the medium when a longi tudinal high-frequency wave was split into two shear lower frequency w aves. The interaction manifested itself by space beat. The envelope wa velength decreased with an increase of the longitudinal wave amplitude . A cubic nonlinearity may cause four-wave resonance interactions of h elical shear waves.