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.