Dynamic-contact stiffness at the interface between a vibrating rigid sphere and a semi-infinite viscoelastic solid

Vibration of a rigid sphere contacting a semi-infinite viscoelastic solid is studied theoretically. The rigid sphere is subjected to an oscillating force while being compressed in the vertical direction by a static force. The contact-pressure distribution and contact radius at the interface vary with the oscillation. Assuming sufficiently small oscillating force, we derive the dynamic-contact-pressure distribution with the constant contact radius, which establishes dynamic contact stiffness between the sphere and the viscoelastic solid. Numerical calculations show the influence of vibration frequency, contact radius, Poisson's ratio, and the damping characteristic of the solid.