THE VISCOELASTIC MOVING-CONTACT PROBLEM WITH INERTIAL EFFECTS INCLUDED

A general integral equation is derived for the problem of a rigid punc h moving across a viscoelastic half-space with inertial effects includ ed. When the half-space is modelled as a standard linear solid, it is shown that the problem is formally equivalent to a non-inertial proble m with the half-space response described by a continuous-spectrum visc oelastic function. The resulting integral equation is solved numerical ly. The pressure function and the coefficient of hysteretic friction a re plotted for various materials. The discussion is restricted to punc h velocities less than the lowest speed of Rayleigh waves in the mater ial. The theory predicts that internal frictional losses, and therefor e hysteretic friction, are low for large and small viscoelastic decay times. In some cases, this gives rise to a hump-shaped curve when hyst eretic friction is plotted against velocity, just as for the non-inert ial theory. However, because hysteretic friction always increases shar ply as the lowest Rayleigh speed is approached, its behaviour as a fun ction of velocity, for some material densities, may be monotonic.