“Sweet Spot” or “Sweet Zone”? Modal Analysis of a Wooden Baseball Bat for Design Optimization

This paper describes modal testing of a wooden baseball bat with the purpose of finding the peak frequencies and vibration modes and their relation to the so-called “sweet spot”. Initial vibration testing was done by performing a tap test along a Louisville Slugger wooden baseball bat. The bat was suspended by elastic rubber bands to approximate free-free boundary conditions. The peak frequencies and bending mode shapes of the baseball bat were obtained. To verify the results, a modal analysis of the baseball bat was performed to simulate the structure’s dynamic behavior. The animated model validated the accuracy of the parameters obtained in the tap test. The bending mode shapes were also compared to the bending elastic mode shapes of a uniform, homogeneous beam undergoing no shear distortion. The exact solution of the beam equation of motion was solved. The mode shapes were plotted to compare them with the ones obtained from the baseball bat. This comparison indicated that the bat and the beam structures presented the same type of bending mode.