FINITE-AMPLITUDE WAVES IN DEFORMED MOONEY-RIVLIN MATERIALS
FINITE-AMPLITUDE WAVES IN DEFORMED MOONEY-RIVLIN MATERIALS
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DOI：
10.1093/qjmam/45.4.575
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发表时间：
1992-11-01
影响因子：
0.9
通讯作者：
HAYES, M
中科院分区：
文献类型：
--
作者：
BOULANGER, P;HAYES, M
在之前的论文 (3) 中，Currie 和 Hayes 表明，两个线性极化的有限振幅剪切波（在彼此正交的方向和传播方向 n 上极化）可以沿着保持在任意静态有限均匀变形状态的 Mooney-Rivlin 材料中的任何方向传播。在这里，我们恢复了这个结果，并根据 n 与特殊方向（称为“声轴”）所成的角度获得了两个波的速度的显式表达式。这是两个波速相等的唯一方向。它们仅由材料的基本静态变形决定。如果这种变形是三轴的，则有两个这样的方向，如果是双轴的，则有一个这样的方向。然后，表明，虽然理论是非线性的，但沿任意方向传播的两个波的叠加也是一种解。特别是，对于沿声轴传播，椭圆偏振和圆偏振有限振幅波是可能的。最后，考虑波的能量通量和能量密度。
In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.Here, we recover this result and obtain explicit expressions for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'. These are the only directions such that the two wave speeds are equal. They are determined only by the basic static deformation of the material. There are two such directions if this deformation is triaxial, and one if it is biaxial.Then, it is shown that, although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution. In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.Finally, the energy flux and energy density of the waves are considered.