Rolling/Sliding of a Vibrating Elastic Body on an Elastic Substrate

The rolling/sliding in the presence of friction of a vibrating elastic body on an elastic substrate is studied. It is shown that the longitudinal components of the velocity of the center of mass of the body and of the resultant frictional force are not affected by the vibration process. However, the normal vibration of the body influences the slip velocities and the distribution of frictional forces. For the problem of a harmonically oscillating long cylinder rolling/sliding on the flat surface of an elastic substrate, the time histories of the width of the contact zone and the length of adhesion subzone are computed. It is shown that the local frictional forces and slip velocities oscillate, and that the set of admissible values of the external frictional forces and moments providing the rolling/sliding regime is smaller under conditions of normal vibrations than that when the cylinder does not vibrate.