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首页> 外文会议>NATO Advanced Research Workshop on Surface Waves in Anisotropic and Laminated Bodies and Defects Detection; 20011030-1102; Moscow(RU) >EDGE WAVES IN THE FLUID BENEATH AN ELASTIC SHEET WITH LINEAR NONHOMOGENEITY
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EDGE WAVES IN THE FLUID BENEATH AN ELASTIC SHEET WITH LINEAR NONHOMOGENEITY

机译：弹性板下流体中的边缘波动，具有线性非均质性

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Edge waves propagating along rectilinear discontinuities in elastic sheet floating on the surface of deep water are investigated. Dispersion curves were found for symmetric edges waves propagating along a crack in an elastic sheet and along an elastic rod joined with the edges of an elastic plate. It is shown that the frequency of edge waves near the crack can be arbitrary small, while the frequency of edge waves near the rod is greater some limiting value depending on the stiffness and density of the rod. It is shown that the shape of the plate deformed by the edge wave near the crack is characterized by two space scales, one of them is related to the damping of wave amplitude far off the crack, and the other characterizes the behavior of bending moments in the vicinity of the crack. The second scale is much smaller the first. Edge waves propagating in rotating half-infinite layer of shallow water beneath an elastic plate are investigated. It is shown that dispersion curve of the Kelvin wave is transformed into the dispersion curve of the edge wave, propagating along a crack in an elastic plate floating on the surface of shallow water, when the wave frequency tends to the infinity. The influence of a depth discontinuity and floating ice cover on dispersion properties of shelf waves and edge waves propagating along the coastline is investigated. It is shown that the shapes of dispersion curves of the sub-inertial shelf waves, Kelvin waves and low frequency edge waves are similar to the dispersion curves of such waves propagating in shallow water with free surface. When the length of ice cover is smaller the distance between the coastline and shelf break there is infinite number of shelf modes. There is only finite number of edge wave modes when ice cover totally occupies region between the coast and the depth discontinuity or when the length of ice cover is greater the distance between the coast and shelf break. Wave numbers of edge waves are smaller limiting value k_O, which is defined by formula (3.6). One finds that when relative changing of water depth is H_0/H_1 - 1 ≈ 0.1 and ice thickness is 1m. Period of this wave is equal to 8.7 sec when H_1 = 30m. Therefore, it is possible to conclude that the influence of floating ice on the waves propagating in coastline region of the depth several tens meters when wave frequency is smaller 0.1 Hz is small.
机译：研究了在深水表面漂浮的弹性片中沿直线间断传播的边波。对于沿弹性片材中的​​裂纹和与弹性板的边缘连接的弹性杆传播的对称边缘波，发现了色散曲线。结果表明，裂纹附近的边缘波的频率可以任意小，而杆附近的边缘波的频率则取决于杆的刚度和密度而具有更大的极限值。结果表明，裂纹附近的边缘波使板的变形具有两个空间尺度的特征，其中一个与离裂纹远的波幅的衰减有关，另一个与弯矩的作用有关。裂缝附近。第二个标度比第一个标度小得多。研究了在弹性板下方旋转的无限半浅水层中传播的边缘波。结果表明，当波频率趋于无穷大时，开尔文波的频散曲线转变为边波的频散曲线，并沿着一条漂浮在浅水表面的弹性板中的一条裂缝传播。研究了深度不连续性和浮冰覆盖对沿海岸线传播的架子波和边波的色散特性的影响。结果表明，亚惯性架波，开尔文波和低频边缘波的频散曲线形状与此类波在具有自由表面的浅水中传播的频散曲线相似。当冰盖的长度较小时，海岸线与架子破裂之间的距离会无限多。当冰盖完全占据海岸和深度不连续之间的区域时，或者当冰盖的长度更大时，海岸和架子破裂之间的距离就只有有限数量的边缘波模式。边缘波的波数是较小的极限值k_O，其由公式（3.6）定义。人们发现，当水深的相对变化为H_0 / H_1-1≈0.1且冰厚度为1m时。当H_1 = 30m时，该波的周期等于8.7秒。因此，可以得出结论，当波频率小于0.1Hz时，浮冰对在数十米深度的海岸线区域中传播的波的影响较小。

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