Surface waves in deformed elastic materials
Surface waves in deformed elastic materials
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DOI：
10.1007/bf00277451
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发表时间：
1961
影响因子：
2.5
通讯作者：
M. Hayes;R. Rivlin
中科院分区：
文献类型：
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作者：
M. Hayes;R. Rivlin
本文应用各向同性弹性材料中有限变形与无穷小变形叠加的理论，研究了在静态、均匀变形下半无限体中表面波的传播。本文首先研究了由雷莱特[21]发现的波类型。可以看出，该运动与Rayleigh根据经典弹性理论所表述的运动没有本质上的不同。正如所预料的那样，不存在色散，因为在物体的尺寸或物体所经历的变形中，都不涉及基本长度。而且，在不存在横向于波的传播方向的位移的意义上，运动是二维的。由于初始的小的纯均匀变形，在这类波的传播频率中，采用了一种等效于MURNAGHAN [3]所用的应变能函数形式来获得修正。RIVLIN [4]所概述的从相应的可压缩体的二阶结果推导二阶弹性理论中不可压缩体的结果的方法，用于以显式形式获得不可压缩体情况下的位移分量。下面讨论在一个半无限体中，在一个纯均匀变形下，具有横向水平运动的表面波的可能性。我们发现，这样的波可能不会在一个主方向上传播，除非施加严格的条件上的应变能函数。然后，按照洛夫[5]，我们假设在半无限体上有一层材料，其性质与半无限体的性质不同，并受到不同的纯均匀变形。主方向在层中被认为与在主体中相同。一个无穷小的变形叠加在复合体和洛夫型波的存在条件寻求。得到的条件与LOVE发现的条件相似。
In the present paper we apply the theory~ 1]* of the superposition of infinitesimal deformations on finite deformations in an isotropic elastic material to the study of the propagation of surface waves in a semi-infinite body which is subjected to a static, pure homogeneous deformation. Waves of the type discovered by RAYLEIGIt [21 are first examined. It is seen that the motion does not differ essentially from that formulated by RAYLEIGH on the basis of classical elasticity theory. There is no dispersion, as might be expected, since no fundamental length is involved either in the dimensions of the body or in the deformations it undergoes. Also, the motion is two-dimensional in the sense that there is no displacement transverse to the direction of propagation of the waves. A form of strain-energy function, equivalent to that used by MURNAGHAN [3], is employed in obtaining the correction, due to an initial small pure homogeneous deformation, in the frequency of propagation of waves of this type. The method, outlined by RIVLIN [4], of deducing the results for an incompressible body in second-order elasticity theory, from the corresponding second-order results for a compressible one, is used to obtain in explicit form the displacement components for the case of an incompressible body. The possibility of having surface waves with transverse horizontal movement in a semi-infinite body, subjected to a pure homogeneous deformation, is next discussed. We find that such waves may not be propagated in a principal direction unless stringent conditions are imposed on the strain-energy function. Then, following Love [5], we assume that there rests on the semi-infinite body a layer of material with properties differing from those of the semi-infinite body and subjected to a different pure homogeneous deformation. The principal directions are taken to be the same in the layer as in the subjacent body. An infinitesimal deformation is superimposed on the composite body and conditions for the existence of Love-type waves are sought. The conditions obtained are similar to those found by LOVE.