请教这类波动方程的边界条件

sghwxfqtd

两端用F力拉一杆，在t=0时刻，右端力释放，请教此过程中（应力波未传到左端）的杆纵向振动方程的边界条件。谢谢

tonnyw

1# sghwxfqtd

In my opinion, this problem is equivalent to the case where one end is fixed and the other end has the force.

The initial conditions is : Initial displacement is zero and likewise initial velocity.
Boundary conditions: at fixed end displacement is zero and at the force end it should be the stress times delta function at t = 0

sghwxfqtd

2# tonnyw
非常感谢兄的回答，我开始是这样做的。但我的初始条件是：初始位移为应变，不为0，初始速度为0。边界条件是：固定端位移为0，另一端端面的应力从t=0时刻开始为0。
与兄之回答相差甚远，特请教。
另，我主要想算当力F释放后产生的应力波第一次到达固定端时的应力和速度
谢谢

sghwxfqtd

继续请教各位，我所想要的结果不能进行tonnyw 前辈的方法化简

tonnyw

2# tonnyw  
非常感谢兄的回答，我开始是这样做的。但我的初始条件是：初始位移为应变，不为0，初始速度为0。边界条件是：固定端位移为0，另一端端面的应力从t=0时刻开始为0。
与兄之回答相差甚远，特请教。
另， ...
sghwxfqtd 发表于 2010-12-17 22:06

For a problem like this, I am pretty sure you can treat it as a 1D problem and get the results by hand calculations.

I am a little bit confused. Should the initial boundary value problem be formulated as shown in the attached figure? But I never had chance play with wave propagation. So I could be wrong.

sghwxfqtd

5# tonnyw
非常感谢您的热心答复，谢谢