Cascade cross modulation due to the nonlinear interaction of elastic waves in samples with cracks

The phenomenon under study consists in that, in an inhomogeneous material with nonlinearity caused by the presence of soft defects (the so-called "nonclassical" nonlinearity), cascade nonlinear effects are fairly strong and may even become comparable to the first-order effects. Similar cascade effects in media with a common nonlinearity of the crystal lattice are much weaker. This difference can be used as an important diagnostic indicator in nondestructive testing. Experimental data obtained for samples with cracks, which exhibit both ordinary modulation and cross-modulation effects, as well as a cascade cross modulation, are presented. The origin of the enhanced level of cascade effects is explained by modeling with the use of a simple model of nonlinearity of an inhomogeneous material containing soft Hertzian contacts.