One-dimensional theory of cracked Bernoulli-Euler beams
One-dimensional theory of cracked Bernoulli-Euler beams
复制标题
DOI：
10.1016/0020-7403(84)90017-1
复制
发表时间：
1984
影响因子：
7.3
通讯作者：
S. Christides;A. Barr
中科院分区：
文献类型：
--
作者：
S. Christides;A. Barr
导出了含有一对或多对对称裂纹的名义均匀Bernoulli-Euler梁的微分方程及其边界条件。在选择合理的应力场、应变场、位移场和动量场之后，通过在横截面上进行积分来实现降维到一维空间。具体地说，裂纹引起的应力扰动是通过一个局部函数来考虑的，该局部函数假定随着距离裂纹的距离呈指数衰减，并且包含一个可以通过实验测试来估计的参数。文中简要介绍了一些模拟裂纹的含切削梁的实验，其一阶固有频率随裂纹深度的变化与理论预测吻合较好。
The differential equation and associated boundary conditions for a nominally uniform Bernoulli-Euler beam containing one or more pairs of symmetric cracks are derived. The reduction to one spatial dimension is achieved using integrations over the cross-section after plausible stress, strain, displacement and momentum fields are chosen. In particular the perturbation in the stresses induced by the crack is incorporated through a local function which assumes an exponential decay with distance from the crack and which includes a parameter which can be evaluated by experimental tests. Some experiments on beams containing cuts to simulate cracks are briefly described and the change in the first natural frequency with crack depth is matched closely by the theoretical predictions.