Forced movement of a ball in spherical cavity under kinematic excitation

In the paper the response of a heavy ball rolling inside a semi-spherical cavity under horizontal kinematic excitation is investigated. The system with six degrees of freedom with three non-holonomic constraints is considered. The contact between the ball and the cavity surface is supposed to be perfect without any sliding. The mathematical model using the Appel-Gibbs function of acceleration energy is developed and discussed. The most important post-critical regimes are outlined and qualitatively evaluated on the frequency axis. Numerical experiments have been performed when excitation frequency is slowly swept up and down. Results obtained by means of semi-analytical investigation and numerical simulation are evaluated and physically interpreted. Some applications in civil engineering as a tuned mass damper used on slender structures is outlined. Strengths and weaknesses of solution method are evaluated