提出并证明了杆件拉伸和振动的中值定理，及逆定理并对所得的结果进行了讨论。

提出并证明了杆件拉伸和振动的中值定理，及逆定理并对所得的结果进行了讨论。的英文翻译

基本释义

• In this paper,the mean value theorem and converse theorem of the pull nd vibration of a bar are presented and proven, and the results obtained are discussed.