热膨胀动态过程的理论和实验研究

Theoretical and Experimental Studies of the Dynamic Process of Thermal Expansion

摘要: 本文列出了一维点阵非谐振动的非线性微分方程组，并求出了这组方程在相应边值条件下的解析解。据此算出了该点阵的热膨胀系数和热膨胀动态过程的特征时间，同时说明了它的物理意义。关于金属箔的实验结果，可以作为这一理论预言的一个验证。这些结果还告诉我们，在高速加热时，即使温度均匀而且膨胀自由，热应力仍然存在，不过将很快弛豫。
- 非谐振动 /
- 热膨胀动态过程 /
- 热膨胀特征时间
Abstract: The exact solutions of a set of non-linear differential equations with limiting conditions describing the anharmonic vibration of a one-dimensional lattice have been obtained. The thermal expansion coefficient of the lattice and the characteristic time of thermal expansion process were found and physical interpretations given. Some experimental results of thin metal foils could be taken as an evidence for the theoretical prediction. These results also tell us that, for high-speed heating, thermal stress exists even in the case of uniform temperature and free expanding, though it relaxes rapidly.
- anharmonic vibration /
- dynamic process of thermal expansion /
- characteristic time of thermal expansion