Fractal Theory-based Damage Diagnoses Method For Beam Structures

Bridges will inevitably cause damage during long-term use.So it is very important to diagnose the damage of bridge and find the location of damage in time with the most appropriate and effective method.Therefore,as one of the most important problems of structural health monitoring,damage diagnosis has been paid more and more attention.It is of great significance to explore the diagnostic methods and schemes of simple and effective and effective bridges.Fractal theory,as an emerging discipline that has developed in recent years,can describe the various things in the natural world that are regular or irregular through a unique fractal dimension,and it tells us the difference in dimensions between various things through digital means and it has great prospects for development.This paper combines the fractal theory with the damage diagnosis of bridges,starting with the vibration modes and accelerations of the most commonly used simple beam and cantilever beam,and based on the previous fractal theory,the analysis and improvement of the bridge diagnosis method,and explore more suitable Diagnostic methods and programs.The main content includes the followings:(1)Analyze the modal identification method based on the damaged bridges of the Katz dimension,and introduce the influence formula of the displacement magnification of the vibration model on the calculation dimension parameter d/L,and make the relationship between the multiple of the original vibration mode determination and d/L.In addition,the image reflects the effect of linear normalization on d/L.Through the combination of finite element software and programming software,the relationship between the damage length and the optimal sampling distance was analyzed.At the same time,the wavy curvature difference method was applied to the modal dimension of the bridge,and a good damage diagnosis effect was obtained.It was also characterized by a small number of magnitudes.It was obtained by simulating the fact that the actual measurement point spacing is much larger than the damage length.Under the single damage condition,the Katz curvature curvature difference method is more applicable.By using the Katz dimension,the difference of the dimension and the curvature difference of the waveform,the damage location of the single damage and multiple damage of the cantilever beam model is carried out,and the conclusion is drawn that the Katz dimension difference and the curvature difference of the waveforms are better,and the difficulty of the damage location becomes larger with the distance from the damage to the beam end.Finally,the normalized difference of the vibration pattern is proposed.The Katz dimension is used to diagnose the damage of large measuring distance and small damage.Comparing the box dimension difference,we get their own advantages and disadvantage.(2)The box dimension is introduced to diagnose the damage of the simple beam by the vertical acceleration of the bridge vibration.By changing the position of the impact force,it is concluded that the effect of the short span beam is better than that of the other exciting positions,and the deficiency of the box dimension curvature difference method in the damage diagnosis is verified by the experiment.The five point distribution scheme of box dimension curvature difference,which is more sensitive to the damage degree,is proposed for the weak point,and the test points with higher sensitivity to the defined weak position are found through the experiment.Finally,the influence of the characteristics of the bridge and the time of excitation on the damage diagnosis of the acceleration and the displacement box dimension is investigated.It is found that when the frequency of the external shock excitation is close to the 1 natural frequency of the structure,the damage diagnosis of the previous sections can not be diagnosed by the box dimension curvature difference,and the previous excitation is in the middle of the span.It is better than excitation in other locations.Therefore,the location and frequency of external excitation can be applied to get the key of time series,which is the curvature of box dimension.Finally,a box dimension damage diagnosis method for frequency displacement and frequency acceleration signals is proposed based on the time series signals,And the damage conditions were diagnosed.