Wave Propagation in Elastic Media
Wave Propagation in Elastic Media
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弹性介质中的波传播
DOI：
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发表时间：
1988
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影响因子：
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通讯作者：
Julian L. Davis
中科院分区：
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作者：
Julian L. Davis
在前几章中，我们研究了波在水中、无粘流体和粘性流体中传播的性质。有人指出，区分一种介质与另一种介质的守恒定律是能量方程。它是包含适当的状态方程或本构方程的守恒定律，它定义了介质。例如，绝热状态方程用于定义诸如空气的流体，而不同的状态方程用于定义水。绝热条件不能用于激波，因为我们必须考虑熵的跳跃等。在前几章中进一步指出，在数学上描述守恒律所用的方法是欧拉表示。这种表示在处理流体的大颗粒运动时更有用。也有人说，守恒定律包含了给定情况的基本物理学，从这个意义上说，从这些守恒方程，即所谓的场方程，我们可以得到速度场、压力场等，这就给出了波的性质。由于场方程是用欧拉坐标表示的，因此由它们的解导出的各种场也被表示为这些欧拉坐标的函数。原则上，我们可以映射回拉格朗日坐标，从而获得粒子轨迹。
In previous chapters we investigated the properties of waves propagating in water and in inviscid and viscous fluids. It was pointed out that the conservation law that distinguishes one medium from another is the energy equation. It is the conservation law that contains the appropriate equation of state or constitutive equation which defines the medium. For example, an adiabatic equation of state was used to define a fluid such as air and a different equation of state for water. The adiabatic condition cannot be used across a shock wave since we must allow for a jump in entropy, etc. It was further pointed out in previous chapters that the approach used in mathematically describing the conservation laws was the Euler representation. This representation is more useful in dealing with large particle motions of the fluid. It was also stated that the conservation laws contain the fundamental physics of a given situation in the sense that from these conservation equations, which are called the field equations, we can obtain the velocity, pressure fields, etc., which give the wave properties. Since the field equations were couched in the Eulerian coordinates, the various fields that were derived from their solutions were also expressed as functions of these Eulerian coordinates. In principle, we can map back into the Lagrangian coordinates and thereby obtain the particle trajectories.