测点间距对曲率模态检测结构损伤的影响分析及解决方法

Influence analysis and solution of measure-point distance on structural damage detection by curvature modal

损伤使结构局部刚度下降,导致损伤位置的曲率出现突变,基于曲率模态突变检测损伤物理意义明确。曲率模态不能直接测量,需要模态振型对测点间距二次差分才能得到,因此测点间距会影响损伤检测的效果。首先,梳理已发表的33个使用曲率模态法检测不同损伤程度的数值模拟算例,统计各模型测点间距与跨径的比值,给出测点间距小于等于损伤长度时的单跨测点间距建议。然后,以某连续梁桥有限元模型为数值算例,通过降低局部单元的弹性模量来模拟损伤,计算不同损伤工况在不同测点间距下的模态振型,由中心差分法计算曲率模态,进一步计算各种曲率模态损伤表征指标。结果表明:当测点间距大于损伤长度时,曲率模态的突变效应被减弱;曲率模态差(MDC)、曲率损伤因子(CDF)、叠加模态挠度曲率(SMDC)、曲率模态变化率(CMCR)四种指标对曲率突变都具有一定的放大效应,其中CDF和CMCR指标各有优劣,可根据实际需要选用,能够在一定范围内解决测点间距变大对曲率模态检测结构损伤的不良影响。

Structural damage makes local stiffness decrease,resulting in a sudden change in curvature at the damage location,so the sudden change based on curvature modal to detect damage has clear physical significance.Since the curvature modal cannot be measured directly,that needs to be obtained by secondary differencing of the vibration modal,so the measure-point distance will affect the effectiveness of damage detection.At first,the 33 published numerical simulation cases using curvature modal method to detect different degrees of damage were reviewed,and the ratio of measure-point distance to span was calculated for each case.The recommendations of measure-point distance for single-span were summarized when the measure-point distance was less than or equal to the damage length.Then,a continuous girder bridge finite element model was used as a numerical example to simulate the damage by discounting the elastic modulus of the local unit.The modal vibration patterns under different damage conditions and measure-point distance were calculated.The curvature modals were calculated by central difference method,and then the damage characterization indexes of various curvature modals were further calculated.The results show that the abrupt change effect of the curvature modals was attenuated when the measure-point distance was larger than the damage length.Modal difference of curvature(MDC),curvature damage factor(CDF),superposition of modal deflection curvature(SMDC),and curvature modal change rate(CMCR)all had a certain amplification effect on the curvature mutation.Among them,CDF and CMCR indicators had their own advantages and disadvantages,these can be chosen according to the actual needs,which can solve the adverse effects of large measure-point distance on the curvature modal detection of structural damage within a certain range.