Direct Index Method Of Damage Detection Based On Strain Mode Shape Of Damage Structure

Theoretical derivation, numerical simulation and model test were synthetically applied in the paper. General damage rules of different-sized simple beams were detailedly studied by model test and numerical simulation. Synthesizing modal parameters, such as natural frequency, strain mode and so on, indirect index method of damage detection is presented. Then, the space principles of measuring point are obtained. Based on strain mode shape (SMS), the direct index methods of damage location and degree detection are presented and founded. The damage of aqueduct was studied by numerical simulation and the direct index methods were proofed. Finally, synthetical methods of damage location and degree detection are provided. Four contents are expounded as follows.(1)The indirect index method of damage detection was detailedly studied by model test and numerical simulation. The general relationships between modal parameters and the damage location or degree of simple beams and aqueduct are obtained. Caused by damage, the change of natural frequencies and displacement modes is small. It is inapplicable to detect node damage using the frequency, displacement mode and strain mode. The strain mode is very sensitive to the non-node damage, especially to the damage nearby the peak value location of displacement mode. There is sharp variation nearby the damage location, and the range of it extends with the damage degree increasing. For the beam, the range is 6.9%～12.5% of the beam length. For the model aqueduct, the natural frequencies and displacement modes are more insensitive to the damage. The range of sharp variation zone at low mode is greater than at higher mode.(2) Based on difference theory of SMS for damage structure, the direct index method of damage location detection is studied. First, the mathematic models of equidistant and inequidistant difference schemes are founded. Then, the range of influence, criteria and process of damage location detection are obtained. The index is also used to detect concrete damage with microcrack, namely without macrocrack. The extreme point of SMS may be inexistent at the damage location, but there is sharp variation in difference curves of it. For the microcrack concrete structure, translation of abscissa axis of difference curves may occur if compared with that of macrocrack concrete structure.(3) Based on local strain mode shape area of damage structure, the direct index method of damage degree detection is studied. First, using the unaffected data of SMS by damage, SMS of undamaged structure is fitted by least squares method and the optimization degree of polynomial is obtained of the first two SMS. Secondly, the mathematic representation of local strain mode shape area is deduced and the direct index method of damage degree detection is founded. Thirdly, four features are induced of simple beams. Finally, the fitting curves between damage degree and direct index of simple beams and aqueduct are obtained.(4) Synthetical methods of damage location and degree detection are provided. According to the results of simple beams and aqueduct, the process of application is...