Modes of Vibration in Basketball Rims and Backboards and the Energy Rebound Testing Device

Abstract

Six mode shapes, including bending and torsion, were documented for five different basketball rims and backboards at the United States Military Academy, West Point, New York, NY, USA. The frequency and damping ratio of each mode shape were also determined. The empirical process began with the time-domain excitation and response of each rim-backboard system. The impulse of excitation came from an impact hammer separately applied sequentially to each node. The sinusoidal response was gathered from an accelerometer at a fixed location (node 1). Each time-domain excitation response was then converted to a frequency-domain Bode plot for each node by a Brüel & Kjær 2034 Signal Analyzer, giving transfer functions of output/input versus frequency. Structural Measurements System (SMS) StarStruc software was used to fit mode shapes to the Bode plots. Each of the six mode shapes was fitted to the Bode plots of each node at a specific modal frequency. Each of the six mode shapes was a function of the locations of the nodes, and the Bode plots gathered at each node. The first and second modes were critical for showing that the Energy Rebound Testing Device statistically correlated with the energy transferred to the rim and backboard. A known perturbation mass was selectively attached to the rim to help isolate the dynamic masses and spring rates for the rim and backboard and to ascertain that the kinetic energy transferred to the rim had a 95.67% inverse correlation with rim stiffness.