Free Vibrations of Beams With a Single-Edge Crack
Free Vibrations of Beams With a Single-Edge Crack
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DOI：
10.1006/jsvi.1994.1058
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发表时间：
1994-02
影响因子：
4.7
通讯作者：
M. Shen;C. Pierre
中科院分区：
文献类型：
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作者：
M. Shen;C. Pierre
摘要推导了含单边裂纹的均匀伯努利-欧拉梁的运动方程及相关边界条件。所采用的广义变分原理允许修改应力、应变和位移场，以满足裂纹附近的相容性要求。应力集中通过在梁的相容关系中引入裂纹函数来表示。引入位移函数来修正裂缝附近的面内位移及其斜率。这两个函数都选择在开裂截面处有其最大值，并沿梁的纵向呈指数衰减。指数衰减率由有限元计算得出。分别用Galerkin法和局部Ritz法求解了单边裂缝简支梁和悬臂梁的运动方程。这些理论固有频率和模态振型与实验和有限元结果非常吻合。讨论了从动力特性变化判断裂纹梁损伤特性的可能性。
Abstract The equation of motion and associated boundary conditions are derived for a uniform Bernoulli-Euler beam containing one single-edge crack. The generalized variational principle used allows for modified stress, strain and displacement fields that satisfy the compatibility requirements in the vicinity of the crack. The concentration in stress is represented by introducing a crack function into the beam's compatibility relations. A displacement function is also introduced to modify the in-plane displacement and its slope near the crack. Both functions are chosen to have their maximum value at the cracked section and to decay exponentially along the beam's longitudinal direction. The rate of exponential decay is evaluated from finite element calculations. The resulting equation of motion is solved for simply supported and cantilevered beams with single-edge cracks by a Galerkin and a local Ritz procedure, respectively. These theoretical natural frequencies and mode shapes match closely with experimental and finite element results. The possibility of determining the damage properties of cracked beams from changes in dynamic behavior is discussed.