Dynamic stability and vibration responses of a volleyball game ball

This study investigates the vibrational response of a graphene oxide-reinforced volleyball under impact loading, aiming to enhance its dynamic stability. Employing Hamilton's principle and spherical shell coordinates, we derive the governing equations for the ball's motion under internal loading. These equations are solved using the generalized differential quadrature (GDQ) method and analytical techniques to analyze the vibrational modes. The results demonstrate a significant correlation between the ball's radius and its dynamic stability, with variations in radius substantially affecting vibrational characteristics. Notably, we find that increased ball mass, independent of size, contributes to enhanced stability upon ground impact. This observation suggests that heavier balls exhibit improved resistance to deformation and vibration, leading to more predictable trajectories. The findings provide a quantitative basis for optimizing volleyball design by elucidating the interplay between material reinforcement, geometry, and impact dynamics, thereby facilitating the development of volleyballs with improved stability and performance.