網球運動為全球最受矚目的運動項目之一，除了運動員的技術之外，使用的器具也不斷革新。網球屬於持拍運動，必須透過球拍完成各種動作，即藉由球拍與球的碰撞將網球發送或反擊給對手。如何設計更好的球拍，使得擊球時能有更大的恢復係數（出射與入射速度量值比）為一重要課題。此外，擊球時的撞擊力道會傳遞至手臂，使持拍手產生不適甚至導致所謂網球肘之運動傷害，因此也需要減低持拍手震動幅度。本研究之目的即為考量增大擊球恢復係數與減小震動幅度，以模擬計算進行球拍之最佳化設計。為確認模擬結果之效度，首先進行實驗測試，以高速攝影機記錄固定拍頭之球拍，受到球撞擊後拍柄所產生之震幅，並以加速規紀錄拍柄震動時之加速度，再以尤拉白努力樑與彈簧結合的系統類比拍面建立模型並模擬。從實測碰撞震幅和加速度與模擬有近似的結果，可確認模型效度。之後再改變球拍模型的單位質量以及J值(EI，即楊氏係數與轉動慣量之乘積)分布，以最佳化運算設計能使拍面產生最小震幅以及最大恢復係數。根據本篇研究之結果，對於球拍設計有以下建議：當球拍總重在0.3kg±10%時，如欲使拍柄震幅最小，須讓越靠近拍柄位置有較高的J值以及靠近拍柄有較高的密度；若是較重視球拍的威力(恢復係數)，則使拍頭有較高的密度，並在球拍首尾兩端有較高的J值為較好之設計。此外，雖然較重的球拍有較高的回彈球速及較低的拍柄震幅，但應考量實際上運動員體能是否可以負擔。

Tennis is one of the most popular sport activities worldwide. With the competitive feature of modern games, the design of the racket is more and more important. The purpose of this study was to use Euler-Bernoulli beam theory and finite difference method to create a simulation model for optimum racket design. To validate the model, two high-speed cameras and an accelerator were used to record the amplitude and acceleration of racket handle (sampling rate at 1000Hz and 4000Hz, respectively). Comparison of the simulation and experimental results showed effectiveness and reliability of simulating ball-racket impact with the present mathematical modeling. The goal of optimum design was to maximize apparent coefficient of restitution (ACOR) and minimize vibration amplitude at the handle. For rackets of 0.3±10% kg, higher density at the tip and greater J value near both ends was suggested by optimization results if the design focused on ACOR performance. On the other hand, higher density and J value near the butt end was suggested if the focus is on decreasing handle displacement.

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