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首页> 外文期刊>Soil Dynamics and Earthquake Engineering >Forced vertical vibration of rigid circular disc buried in an arbitrary depth of a transversely isotropic half space
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Forced vertical vibration of rigid circular disc buried in an arbitrary depth of a transversely isotropic half space

机译：埋入横向各向同性半空间任意深度的刚性圆盘的强迫垂直振动

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This paper is concerned with the investigation of the vertical vibration of a rigid circular disc buried at an arbitrary depth in a transversely isotropic half space in such a way the axis of material symmetry of the half space is normal to the surface of it and parallel to the vibration direction. By using the Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations called dual integral equations, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration, the governing integral equation is numerically solved in the general dynamic case. Two degenerated cases (ⅰ) the disc is buried in a transversely isotropic full space, and (ⅱ) rigid circular disc is attached on the surface of the half space are discussed. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly found. It is shown that the vertical pressure and the compliance function reduced for isotropic half space are identical to the previous solutions reported in the literature. The dynamic contact pressure under the disc and the impedance function are numerically evaluated in general dynamic case and graphically shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. In addition, the impedance functions evaluated here for the isotropic domain are collapsed on the solution given by Luco and Mita. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared.
机译：本文涉及以一定深度埋入横向各向同性的半空间中的刚性圆盘的垂直振动的研究，即半空间的材料对称轴垂直于其表面并平行于其表面振动方向。通过使用汉克尔积分变换，混合边值问题被转换为一对称为对偶积分方程的积分方程，通常可以将其简化为第二类Fredholm积分方程。借助复杂变量或轮廓积分，可以在一般动态情况下以数值方式求解控制积分方程。讨论了两个退化的情况（ⅰ）将圆盘掩埋在横向各向同性的全空间中，并讨论了（ⅱ）刚性圆盘附着在半空间的表面上。通过解析求解对偶积分方程的简化静态情况，并明确找到垂直位移，接触压力和静态阻抗/柔度函数。结果表明，各向同性半空间的垂直压力和柔度函数减小与文献中报道的先前解决方案相同。在一般的动态情况下，对圆盘下的动态接触压力和阻抗函数进行了数值评估，并以图形方式显示了圆盘边缘的接触压力中存在的奇异性与静态情况相同。另外，在Luco和Mita给出的解中，此处评估的各向同性域的阻抗函数被破坏。为了显示不同材料各向异性的影响，对一些不同的横向各向同性材料进行了数值评估并进行了比较。

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