Empirical Modal and Theoretical Finite Element Analyses of Basketball-Rim Parameters versus Changes in Inflation Pressure

The goal of this study was to quantify the sensitivity of the radial spring rate of a basketball, and the damping ratios of the first two modes of vibration of the basketball interacting with a Gared rim, to the change of inflation pressure. The chosen method of empirical modal analysis was impulse-response, where taps of an impact hammer provided the excitation and an accelerometer measured the response. The ANSYS 2025R1 Workbench modal analysis system was used to compliment the empirical modal analysis, by providing additional insight regarding the first two modes of vibration of the basketball-rim system. Our hypothesis was that the radial spring rate of the basketball would have a high positive correlation, and the damping ratios of the first two modes of vibration of the basketball and rim would have a high negative correlation, with respect to basketball inflation pressure. This study introduced studying the rotation of the modal eigenvectors with respect to the change of inflation pressure to better understand the physics of basketball-rim vibrations.