Vibration Analysis of a Cracked Beam on an Elastic Foundation
Vibration Analysis of a Cracked Beam on an Elastic Foundation
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DOI：
10.1142/s0219455415500066
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发表时间：
2016-04
影响因子：
3.6
通讯作者：
Ali C. Batihan;F. Kadioglu
中科院分区：
文献类型：
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作者：
Ali C. Batihan;F. Kadioglu
考虑了帕斯捷尔纳克和广义弹性地基上矩形截面裂纹梁的横向振动。欧拉-伯努利 (EB) 和铁莫申科梁 (TB) 理论均被使用。开放边缘裂纹表示为旋转弹簧，其柔量通过断裂力学获得。通过应用裂纹位置梁段之间的相容条件和边界条件，推导出特征方程，并以特征方程为根求解无量纲固有频率。给出了示例数值结果，显示了裂缝深度、裂缝位置、基础类型和基础参数对梁的固有频率的影响。据观察，裂缝的存在降低了固有频率，而基础的弹性增加了系统的刚度，从而增加了固有频率。还观察到，弹性基础的类型对裂纹梁的固有频率有显着影响。
The transverse vibrations of cracked beams with rectangular cross sections resting on Pasternak and generalized elastic foundations are considered. Both the Euler–Bernoulli (EB) and Timoshenko beam (TB) theories are used. The open edge crack is represented as a rotational spring whose compliance is obtained by the fracture mechanics. By applying the compatibility conditions between the beam segments at the crack location and the boundary conditions, the characteristic equations are derived, from which the nondimensional natural frequencies are solved as the roots. Sample numerical results showing the effects of crack depth, crack location, foundation type and foundation parameters on the natural frequencies of the beam are presented. It is observed that the existence of crack reduces the natural frequencies, whereas the elasticity of the foundation increases the stiffness of the system and thus the natural frequencies. It is also observed that the type of elastic foundation has a significant effect on the natural frequencies of the cracked beam.