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A damage index, used to identify possible locations and corresponding severities of local damage, is defined and expressed in terms of modal displacements that are obtained numerically from mode shapes of the undamaged and the damaged structures.


Based on a small damage assumption, a damage index equation is revealedn the context of elasticity.


It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes.


With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the Haar wavelet space.


Next, the physical desired solution to the damage index equation is reconstructed from the one in the wavelet space.

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 Modal analysis technology draws more and more attention in the development of structural damage detection. In this paper, the sensitivities of several multiple damage detection methods were calculated. A cantilever beam of rectangular crosssection was studied by using modal analysis experimentally. The shift of modal frequency caused by structural damage was analyzed. The methods above mentioned were applied to the experiments and their efficiency were demonstrated through several damage simulations. Principal... Modal analysis technology draws more and more attention in the development of structural damage detection. In this paper, the sensitivities of several multiple damage detection methods were calculated. A cantilever beam of rectangular crosssection was studied by using modal analysis experimentally. The shift of modal frequency caused by structural damage was analyzed. The methods above mentioned were applied to the experiments and their efficiency were demonstrated through several damage simulations. Principal shortcomings in these methods were also discussed. The results indicated that the strain index is more sensitive to damage than the displacement one for bending structures.  从理论上计算了几种多位置损伤检测方法对结构刚度的敏感度,选用工程上常见的矩形等截面悬臂梁,通过实验模态,对梁损伤引起的模态频率迁移进行了分析,从实验角度对这几种方法的敏感性和有效性进行了比较,并就它们在实际应用中的不足之处进行了讨论。实验结果表明,基于应变模态的损伤指标对承弯结构的损伤更敏感。  Conventional methods using frequency response functions are effective to detect single damage, but are difficult to identify multiple damage locations and extents. In order to solve this problem, a twostage method using incomplete frequency response functions is presented. The damage detection strategy is to localize the damage locations by using damage index of different nodes or degreeoffreedoms, which can be obtained from measured incomplete frequency response functions. A damage quantification formula... Conventional methods using frequency response functions are effective to detect single damage, but are difficult to identify multiple damage locations and extents. In order to solve this problem, a twostage method using incomplete frequency response functions is presented. The damage detection strategy is to localize the damage locations by using damage index of different nodes or degreeoffreedoms, which can be obtained from measured incomplete frequency response functions. A damage quantification formula is then deduced from the reduced degreeoffreedom system to calculate damage extents. The simulation results demonstrate the excellent performance of the proposed twostage method based on degreeoffreedoms damage index to detect multiple damages as compared with other methods.  传统的频响函数损伤探测方法对单损伤识别效果明显,却难于精确识别多损伤情况。为了解决结构的多损伤位置识别和损伤程度的判定问题,将不完备的频率响应函数应用于结构的损伤检测研究,并提出了一种两阶段的损伤识别方法。首先,利用不完备的频率响应函数确定相应的损伤指标,并通过不同节点和自由度处损伤指标的改变来分别初步判断损伤的位置;然后,推导分析了损伤程度计算公式,利用该公式可以精确的计算出相应损伤单元的损伤程度。仿真结果表明,通过自由度损伤指标的改变可以较为精确的识别出损伤的位置,优于节点损伤指标判别法,而通过损伤定量公式不仅可以得到损伤程度的量化值,而且可以更精确的判断损伤的位置。  
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