  The present paper is devoted to a theoretical analysis of sliding friction
under the influence of oscillations perpendicular to the sliding plane. In
contrast to previous works we analyze the influence of the stiffness of the
tribological contact in detail and also consider the case of large oscillation
amplitudes at which the contact is lost during a part of the oscillation
period, so that the sample starts to "jump". It is shown that the macroscopic
coefficient of friction is a function of only two dimensionless parameters - a
dimensionless sliding velocity and dimensionless oscillation amplitude. This
function in turn depends on the shape of the contacting bodies. In the present
paper, analysis is carried out for two shapes: a flat cylindrical punch and a
parabolic shape. Here we consider "stiff systems", where the contact stiffness
is small compared with the stiffness of the system. The role of the system
stiffness will be studied in more detail in a separate paper.
