扭振超声变幅杆截面函数的理论推导

Derivation of Generatrix Functions of the Torsional Ultrasonic Angle Amplitude Transformers

通过对扭转振动方程解的分析,导出使扭转振动方程具有函数解的各种变幅杆的截面函数式.除使以住研究过的指数型、类圆锥型、类悬链线型和阶梯型杆的截面函数得到证明外,还导出了类余弦型和双曲正割型两种新杆型。

The generatrix functions of torsional ultrasonic angle vibration amplitude trasformers for which the function solutions of torsinal vibration equation may be obtained are derived from analysing the solution of torsional vibration equation. In addtion to the generatrix functions mentioned on a previous occasion such as exponential, similar-coni cal, similer-catenary and stepped horns are verified, two new ones——similar-cosine and hyperbolic secant are introduced.