On exact wave propagation analysis in a beach volleyball ball

Wave propagation and vibration state in the sports balls have important effects on the stability in movement and accuracy of hits. In some sports, similar to football and volleyball, the balls are subjected to continuous strong hits from players. In the current study, the wave propagation in a beach volleyball ball under the effect of temperature change, different material characteristics, different thicknesses, and the total mass is investigated. In this regard, the ball is modeled using a spherical shell structure and a higher-order displacement field is considered. The classical theory of elasticity is employed along with Hamilton's principle for the spherical shell. The outcome equations with different boundary conditions are solved by engaging the discrete singular convolution method (DSCM). In addition, the finite element method is used to obtain the modal shape and natural frequency. The formulations and solution method are utilized in different steps of convergence examination, validation, and parametric study to acquire a comprehensive insight into the behavior of beach volleyball balls under the effect of the dynamic loading conditions. In specific, we are more interested in the phase velocity of the ball. The results are presented for different temperature changes and geometrical and material properties.