脉冲波在非色散、非耗散弹性媒质中的机械能和动量

本文通过机械能、机械动量流动的观点,依据波传播的线性理论,审查了在一个绷紧不变的弹性弦上或在一个纤细弹性杆中传播的脉冲波。本文建立了能量和动量流动的连续性方程,还导出了波位移的两个边界条件。并且仔细检验了一个重要的特殊情况:就是任意形状的小振幅脉冲通过一个均匀狭窄媒质传输进入到另外一种线性质量密度媒质的状况。本文获得了瞬时入射、反射和透射波脉冲的机械能和动量,并且证明此机械能和动量分别为运动常数。

Mechanical Energy and Momentum of Wave Pulses in a Dispersion Less,Lossless Elastic Medium

In this paper,we re-examine the linear theory of wave propagation through an elastic string under uniform tension or a slender elastic rod from a perspective that focuses on the flow of mechanical energy and mechanical momentum.Continuity equations are established for the flow of energy and momentum,leading to two boundary conditions for the net wave displacement.The important special case of a small amplitude pulse of arbitrary shape traveling through a uniform slender medium joined to another medium with a different linear mass density is examined in detail.The new boundary conditions lead to the correct relative amplitudes for the reflected and transmitted pulses.We obtain the instantaneous mechanical energy and momentum of the incident,reflected,and transmitted pulses and show that the net mechanical energy and momentum are separate constants of motion.