The viscoelastic moving-contact problem with inertial effects included

Abstract

A general integral equation is derived for the problem of a rigid punch moving across a viscoelastic half-space with inertial effects included. When the half-space is modelled as a standard linear solid, it is shown that the problem is formally equivalent to a non-inertial problem with the half-space response described by a continuous-spectrum viscoelastic function. The resulting integral equation is solved numerically. The pressure function and the coefficient of hysteretic friction are plotted for various materials. The discussion is restricted to punch velocities less than the lowest speed of Rayleigh waves in the material. The theory predicts that internal frictional losses, and therefore hysteretic friction, are low for large and small viscoelastic decay times. In some cases, this gives rise to a hump-shaped curve when hysteretic friction is plotted against velocity, just as for the non-inertial theory. However, because hysteretic friction always increases sharply as the lowest Rayleigh speed is approached, its behaviour as a function of velocity, for some material densities, may be monotonic.