Vibration Analysis of an Isotropic Elastic Sphere Contacting a Semi-Infinite Cubic Solid

Vibration analysis of an isotropic elastic-sphere oscillator contacting a semi-infinite cubic solid is investigated by considering dynamic deformation at the contact interface. Assuming sufficiently small oscillation amplitude of the sphere compared with the static indentation deformation, the dynamic maximum contact pressure and the variable contact radius yield a dynamic-contact pressure distribution of constant contact radius. The combination of the sphere oscillation and the solid motion at the contact interface through contact-displacement conditions gives resonance frequencies of the elastic sphere. Unlike the conventional quasi-static model, this dynamic contact model agrees well with the measurements, which will benefit the quantitative evaluation of the local Young's modulus and the orientation of micro-scaled anisotropic grains by the resonance-frequency shifts of a vibrating oscillator in resonance ultrasound microscopy and the efficient removal of micron or sub-micron particles from the substrate in the dry laser cleaning technique.