2014年数学建模美国赛获奖优秀论文.doc

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number7238 ? Problem ChosenA For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ Summary This paper describes model testing of baseball bats with the purpose of finding the so-called “sweet spot”. We establish two models and solve three problems. Basic model describes sweet spot which isn’t this spot at the end of the bat and helps explain this empirical finding. It predicts different behavior for wood (usually ash) or metal (usually aluminum) bats and explains Major League Baseball prohibits metal bats. Improved model proves that corking a bat enhances the sweet spot effect and explains Major League Baseball prohibits corking. Selected methodologies currently used to assess baseball bat performance were evaluated through a series of finite element simulations. According to the momentum balance of the ball-bat system, basic model equation was established. The sweet spot can be found by the solution of the equation, when the baseball bat performance metrics were defined, considering initial variation in speed, the momentum of the bat and ball. Then, the improved model illustrates the vibrational behavior of a baseball bat and finds the peak frequencies and vibration modes and their relation to the “sweet spot”. From these observations two recommendations concerning bat performance were made: (1) This spot isn’t at the end of the bat. The bat is related to materials out of which it is constructed. This model can predict different behavior for wood or metal bats. That is why Major League Baseball prohibits metal bats. (2) In Improved model, a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhance the “sweet spot” effect. This explains why Major League Baseball prohibits “corking”. In some sense we have come full circle to the probl