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用扩展 Dirac函数来表示空心板材在刚度以及质量密度上由于空洞而引起的非连续变化 ,从而变不连续函数的求解问题为连续函数的求解问题 ,继而用 Galerkin法对其固有频率进行了求解 ,得到了适应于任意大小、任意分布空洞的空心板材的固有频率计算公式。计算结果显示 :空心板材的固有频率不仅与板材的几何尺寸有关 ,而且还与各空洞的位置即分布方式有关 ,除此之外还与混凝土的 Poisson比有关
The extended Dirac function is used to represent the non-continuous change of the hollow plate in the stiffness and mass density due to the cavity, so that the solution of the discontinuous function is the solution of the continuous function, and then the natural frequency is solved by the Galerkin method. The natural frequency formula of hollow slab which is suitable for arbitrary size and random distribution is obtained. The calculation results show that the natural frequency of hollow slab is not only related to the geometrical dimension of the slab, but also to the location of each cavity, that is to say, the distribution of the slab. In addition, it is also related to the Poisson ratio