Incident Waves Abstract
Friction Reduction in the Sliding of an Elastic Half-Space
Against a Rigid Surface Due to Incident Dilatational Waves
G.G. Adams
Abstract
The steady sliding of a flat homogeneous and isotropic elastic half-space
against a flat rigid surface, under the influence of incident plane
dilatational waves, is investigated. The interfacial coefficient of
friction is constant with no distinction between static and kinetic
friction. It is shown here that the reflection of a harmonic wave
under steady sliding consists of a pair of body waves (a plane
dilatational wave and a plane shear wave) radiated from the sliding
interface. Each wave propagates at a different angle such that the
trace velocities along the interface are equal and supersonic. The
angles of wave propagation are determined by the angle of the incident
wave, by the Poisson's ratio, and by the coefficient of friction. The
amplitude of the waves are indeterminant, subject only to the
restriction that the perturbations in interface contact pressure and
tangential velocity satisfy the inequality constraints for unilateral
sliding contact.
It is also found that an incident rectangular wave can allow for
relative sliding motion of the two bodies even with a ratio of remote
shear to normal stress which is less than the coefficient of friction.
Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due
to periodic stick zones which propagate supersonically along the
interface. Under appropriate conditions, the bodies can move
tangentially with respect to each other in the absence of an applied
shear stress. The influences of the angle, amplitude, and shape of the
incident rectangular wave, the interfacial friction coefficient, the
sliding speed, and of the remotely applied normal stress, on friction
reduction are determined.
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