【摘要】 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比有关更多还原

【Abstract】 This paper proposes a simple method for calculating the natural frequencies of rectangular plates with cylindrical voids that arbitrarily positioned and illustrates its usefulness by optimizing the natural frequencies.The discontinuous variations in rigidity and mass density of plate that are induced by the voids are expressed by using the extended Dirac function.The natural frequency coefficients of the plate with voids are found to depend not only on the dimensions of the plate and the sizes as well as locations and dispositions of the voids,but also on Poisson’s ratio of plate material.It is pointed in the paper that voids locations and radii can be optimally designed to get the natural frequencies we want.Furthermore,a very simple formula is extended to derive approximate values of the higher order natural frequencies for plates with cylindrical voids.更多还原