Dynamics of Vibration Isolation System with a Ball Vibration Absorber

The forced vibrations of a mechanical vibration isolation system consisting of a ball vibration absorber (BVA) with linear viscous resistance and a movable carrier body under an external harmonic load are considered. Appell's formalism is used to formulate and numerically solve the equations of combined motion of the heavy ball without sliding in the spherical cavity of the carrier body. The frequency response of the system and curves of the maximum amplitude of vibrations of the carrier body versus the radius of the spherical cavity and the coefficient of viscous resistance of the BVA are plotted. The conditions and constraints on the rolling of the heavy ball in the spherical cavity without sliding are established.