Identification of multiple cracks in beams under bending
Identification of multiple cracks in beams under bending
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DOI：
10.1016/j.ymssp.2006.03.008
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发表时间：
2006-10
影响因子：
8.4
通讯作者：
A. Chasalevris;C. Papadopoulos
中科院分区：
文献类型：
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作者：
A. Chasalevris;C. Papadopoulos
梁上横向裂纹的识别是许多研究者的课题。识别裂缝意味着找到它的位置和深度。在许多情况下，梁上有不止一个裂纹。然后，表征裂纹的参数的解或组合更多，并且问题变得更复杂，特别是当必须使用另一个参数（相对于彼此的角位置）来识别裂纹时。本文研究了含两条横向表面裂纹梁的动力特性。每个裂纹的特征在于其深度、位置和相对角度。这两个裂纹都被认为是位于相对于梁的纵向轴线的任意角位置，并且位于距左端的任意距离处。两个自由度的局部柔度矩阵，在水平和垂直平面的弯曲被用来模拟旋转的横向裂纹在轴和计算的基础上的应力强度因子的可用表达式和相关的应变能释放率的表达式。首次计算任意旋转角度下的柔度矩阵。因此，柔度作为裂纹深度和角位置的函数给出。由于应力强度函数的限制，这些表达式仅适用于裂纹零角位置周围的有限区域，而不是每个裂纹角。对于这些情况，B样条曲线被用来插值已知点，并给出了一个函数的解析形式为每个裂纹深度和角度。众所周知，当结构（如梁）中存在裂纹时，则振动的固有频率降低。这种减少在这里研究了六个独立的参数，即深度，位置，和每个裂纹的旋转角度。通过保持这六个参数不变，可以计算和绘制前三个弯曲本征模式。由于小波理论对坡度或位移变化的敏感性，本文采用小波理论来识别裂缝的位置，从而减少了独立参数的数量。众所周知，弯曲梁上裂纹的存在，在梁的弹性线上产生了一个斜率不连续性，该斜率不连续性一般与裂纹深度相似，在此还与角位置相似。在某些情况下，对结构的振型或振动响应进行小波变换，可以用来定位裂纹。如果位置是已知的，则可以确定深度和相应的角度。在这里，前三个特征值与裂纹深度和旋转角度的关系图，用于识别两个裂纹的其余未知参数。
The identification of a transverse crack on a beam is the subject of many investigators. Identifying the crack means to find its position and depth. In many cases there are more than one cracks on a beam. Then the solutions, or the combinations of parameters characterising the cracks are more and the problem becomes more complicated particularly when the crack must be identified using one more parameter, the relative each other angular position. In the present paper the dynamic behaviour of a cracked beam with two transverse surface cracks is studied. Each crack is characterised by its depth, position and relative angle. Both cracks are considered to lie in arbitrary angular positions with respect to the longitudinal axis of the beam and at any distance from the left end. A local compliance matrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model the rotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. The compliance matrix is calculated for the first time at any angle of rotation. Thus, the compliance is given as a function of both the crack depth and the angular location. These expressions are usable, due to the stress intensity function limitations, only for limited regions around the zero angular position of the crack and not for every crack angle. For these cases, B-spline curves are used to interpolate the known points and a function in analytical form is given for every crack depth and angle. It is well known that when a crack exists in a structure, such as a beam, then the natural frequency of vibration decreases. This reduction is studied here for six independent parameters namely the depth, the location, and the rotational angle of each crack. By keeping these six parameters constant, the first three flexural eigenmodes can be computed and plotted. Due to its sensitivity in slope or displacement changes the theory of wavelets is used here to identify the locations of the cracks reducing thus the number of independent parameters. As it is well known the existence of a crack on a beam in bending, creates in the elastic line of the beam a slope discontinuity analog generally to the crack depth and additionally here to the angular position. The wavelet transformation of a vibration mode or of the vibration response of the structure under some circumstances could be used to locate the cracks. If the positions are known, then the depths and the respective angles can be determined. Here the diagrams of the first three eigenvalues versus both the crack depth and the rotational angle, are used to identify the remaining unknown parameters for both cracks.