简文梁爆破后横振动的解析解

On the Analytic Solution of Horigontal Vibration After a Frec Beam Demolich

本文以实验条件和弹性理论,建立了简支梁横振动的边值问题。由于边值问题中的泛定方程不是标准的波动方程,边界条件又是非齐次的,求解问题具有一定的困难。为此首先造一个函数,使边界条件齐次化,然后用冲量定理法和两次迭加原理,巧妙地求出本征函数。在求解过程中为之改善积分计算,多次利用误差函数。其解中含有误差函数的项可作为一级近似。这样比数值计算直观和方便,其结论对材料科学在力学性能的研制上具有一定的理论参考价值。

Using the theory of elasticity and the experimental conditions, this artical establishs a boundary - value problems of ahonizonfal vibration of a free beam, Owing to the general aquation of a boundary - value probleus is not stan- dard wave equation and thebonndary condition is also non - homogeneeus, As a reoult resolving problem has certain diffi- cult. For this renson I first find out a function to enable homogeniying the boundany conditions and then obtain tricky eigenfunction by method of inpulse theerem and two times supperposition principle. Doning resolving process. I use errer function for many times. In ordir to improve integral calculation. ltsanalytic solution contains contains a term of error func- tion. That is a ene - lever approxmate. So it is more obgetine and convenient then numerical method. The conclusion has certain reference value to the development of mechanical properties of inaterial science.