The virtual friction of a sphere vibrating in an elastic medium
The author studies a basic model of elasto-dynamic interaction: A rigid sphere is completely immerged in a surrounding isotropic linear elastic medium and oscillates harmonically. Two special cases are considered: Pure translational and pure rotational vibrations, respectively. A solution method due to Lamb is used for the calculation of the force (torque) which must be applied to the sphere in order to maintain the assumed translational (rotational) harmonic motion. This force (torque) consists of an elastic part and a virtual viscous (frictional) part. Additionally the energy lost due to the generation of elastic waves is calculated and conditions for the existence of aperiodic motions are established.
surrounding isotropic linear elastic medium
scientific article; zbMATH DE number 4072539