【摘要】 本文研究平面激波在活塞上的正反射问题。当激波遇到固壁时,立即发生反射现象。我们假设固壁很薄,忽略内部的弹性波和塑性波,把固壁看成刚体的活塞。当固壁遇到入射波的冲击时,就产生加速度而运动。我们研究在反射初期,由于固壁（活塞）运动所产生的效应。我们采用点爆炸的自模拟解（平面波）作为入射波。本文将反射区物理量展成泰勒级数,以使偏微分方程粗化为线性代数方程组,从而求得解的一级近似表达式。最后给出两个例子,结合例子分析了在反射初期,由于固壁运动所产生的效应。计算结果说明,固壁运动效应的大小决定于固壁的无量綱的初始加速度α₂（α₂=（ω₀t²₁）/R₀,其中ω₀为固壁初始加速度,R₀为爆炸中心位置至固壁的距离,t₁为爆炸开始至波到达固壁所需的时间。）当|α₂|很小时（|α₂|≤0.5）,固壁运动的效应是很微小的。更多还原

【Abstract】 In this paper, we study the problem of the normal reflection of the plane shock wave on the piston. When the shock wave meets with the wall, the reflection phonomenon occurs immediately. Here we suppose that the wall is very thin, and we neglect its internal elastic and plastic waves, and thus consider it as a rigid piston. When the wall is shocked by the incident wave, it obtains an acceleration and moves. We study tne effect produced by the motion of the wall（piston）in a short time from the beginning. We use the auto-model solution （plane wave） of sharpened explosion for incident wave. We develop the physical quantities in the region of reflection into Taylot’s series, and thus transform the system of partial differential equations obtained into a system of linear algebraic equations, and hence obtain the expressions of first approximation solution. Finally, we give two examples with which we analyze the effect produ ced by the motion of the wall in a short time from the beginning. The results obtained by calculation show that the magnitude of the etfect by the motion of the wall is determined by the non-dimensional initial acceleration of the wall: α₂（α₂=W₀t₁²/R₀, where w₀ denotes the initial acceleration of the wall, R₀ the distance of tne center of explosion from the wall, t₁ the time that the wave needs to reach the wall from the beginning of explosion.） When |α₂| is very small （|α|≤0.5）, the effect by the motion of the wall is very small.更多还原