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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack
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Dynamic interaction of plates in an inhomogeneous transversely isotropic space weakened by a crack

机译：平板在不均匀的横向各向同性空间中的动态相互作用被裂缝削弱

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摘要

The problem of axisymmetric vibration of a flat thin rigid circular plate located inside a vertically exponentially graded, transversely isotropic material of infinite extent is addressed by means of a displacement potential method. The contact condition on one side of the foundation is assumed to be the perfect adhesion with the media but known to be faced by a penny-shaped crack at the other side as it occurs in anchors. The mixed boundary value problem is formulated with the aid of Hankel integral transforms and is written in the form of a set of singular integral equations. The analytical procedure for the special case of vertical movement of the rigid plate results in a closed form solution. The solution is pursued numerically for the general elastodynamic case. The physical quantities, such as contact stress on the plate and the stress and displacement fields in the non-homogeneous medium are obtained for different materials.
机译：通过位移电位方法解决了位于垂直指数分级的扁平薄刚性圆形板的轴对称振动的问题。 假设基础一侧的接触条件是与介质的完美粘附，而是已知在另一侧的一分钱形状裂缝面对，因为它发生在锚固中。 混合边值问题是借助于Hankel积分变换的借助配制，并且以一组奇异积分方程的形式写成。 刚性板垂直运动的特殊情况的分析过程导致封闭的溶液。 该解决方案是针对一般弹性动力学案件的方式进行数值追求。 为不同的材料获得了板块上的物理量，例如在板上的接触应力和非均匀介质中的应力和位移场。

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