Analytical and numerical modelling of the nonlinear interaction of shear wave
with a frictional interface is presented. The system studied is composed of two
homogeneous and isotropic elastic solids, brought into frictional contact by
remote normal compression. A shear wave, either time harmonic or a narrow band
pulse, is incident normal to the interface and propagates through the contact.
Two friction laws are considered and their influence on interface behavior is
investigated : Coulomb's law with a constant friction coefficient and a
slip-weakening friction law which involves static and dynamic friction
coefficients. The relationship between the nonlinear harmonics and the
dissipated energy, and their dependence on the contact dynamics (friction law,
sliding and tangential stress) and on the normal contact stress are examined in
detail. The analytical and numerical results indicate universal type laws for
the amplitude of the higher harmonics and for the dissipated energy, properly
non-dimensionalized in terms of the pre-stress, the friction coefficient and
the incident amplitude. The results suggest that measurements of higher
harmonics can be used to quantify friction and dissipation effects of a sliding
interface.Comment: 17 pages, 10 figure
