Research On Damage Identification Of Fatigue Crack In Beam Under Harmonic Excitation

As an important part of modern transportation system,bridge structure plays a very important role in improving the speed of transportation and promoting the development of society and economy.The health status of the bridge structure is closely related to the social economy development,people’s life and property safety.The safety and reliability of the bridge structure have been paid more and more attention.However,during the service period of bridge structure,the damage can’t be avoided under the influence of internal and external factors with the increasing traffic volume,the external environment load,the aging behavior of material,etc.what’s more,the damage will accumulate and expand with the passage of time which can weaken the structural resistance and adverse social impact.Therefore,it is of great practical significance to use the effective technical means discovering the damage of the bridge structure in time and carry out the safety evaluation.Under the external load,the crack is the main form of damage.It will gradually experience from less to more,from small to large.The initial crack shows contactseparation breathing phenomenon with the structure vibration,which is a typical nonlinear fatigue(breathing)cracks.Fatigue crack will change into an always open state because of a large mass of accumulation and expansion of the damage and a significant decline in stiffness,which makes the structure will faces a threat of damage.Therefore,it is valuable to ensure the safety of the structure by means of effectively identifying the damage in the fatigue crack stage and taking appropriate technical measures to prevent the crack make further accumulation and expansion.The traditional dynamic characteristic index is suitable for the identification of linear damage.It is not sensitive to the damage of the fatigue stage which will cause the damage information missing or lost and obtain the wrong damage recognition result.The harmonic excitation response can better describe the fatigue damage nonlinear characteristics.Therefore,in this paper for the fatigue cracked cantilever beam,supported by National Natural Science Foundation of china,based on the nonlinear vibration theory of the structure under the harmonic excitation,systematically analyzing the nonlinear effect of the cantilever vibration under different damage conditions,and then propose the nonlinear damage indicators under harmonic response.after that it is proposed a novel to complete the quantitative identification of damage through the particle swarm optimization vector regression algorithm on the basis of damage location by using vibration mode derived index.The specific research work is as follows:1.The bilinear spring model is used to simulate the fatigue damage,and then analyze the influence of the damage depth and position on the vibration response,on the basis of which the nonlinear damage indicators under harmonic excitation are proposed and the validity is verified.Firstly,the comparative analysis is carried between the integrity and damaged structure on the harmonic vibration response diagram(acceleration time history curve,phase spectrum and power spectrum).It is proved that the model can represent the existence of fatigue damage and has sufficient sensitivity to the harmonic vibration response.Then,the influence of damage depth and damage position on the harmonic response of the structure is discussed,which shows that the more close to the fixed end or the deeper depth of the crack,the more obvious of nonlinear vibration characteristics of distortion,including the excursion of phase spectrum,super/sub-harmonic components of power spectrum,etc.Finally,we establish the nonlinear damage indicators,including the distortion value of the phase spectrum,the breeding value of the harmonic energy and the breeding value of the total energy.The validity and rationality of the results are proved by the discussion of the results.2.The nonlinear contact model has been adopted here to simulate the fatigue damage by considering the time-varying stiffness which is more close to the actual.The influence of the damage depth and position on the response of harmonic vibration is analyzed.Then verify the validity of the nonlinear damage indicators based on the harmonic excitation response.After that the comparison about the recognition effect between the bilinear and nonlinear fatigue damage models has been conduct.First,through the analysis of the harmonic response between the integrity and damaged structure,it is proved that the model is effective for the fatigue damage and sensitive to the harmonic vibration response.Then the vibration response analysis of different damage depth and location is analyzed.The results show that with the damage degree increases the nonlinear dynamic characteristics are more obvious.After that through the calculation and analysis,the nonlinear damage indicators are verified that they can effectively identify the fatigue damage.Finally,on the basis of the above results,the recognition results of the bilinear and nonlinear models are analyzed and compared under the same conditions based on the nonlinear damage indicators.The comparison results show that the nonlinear contact model exhibits more nonlinearity,which is more suitable for the simulation of fatigue damage.3.A new method for quantitative identification of fatigue crack fracture location and damage degree is proposed based on the vibration index and particle swarm optimization support vector algorithm.Firstly,according to the modal vibration data of the fatigue crack cantilever beam,we construct the indicators of the curvature and variable value on the mode shape,on the basis of that the location of fatigue crack has been determined.The particle swarm optimization support vector regression algorithm is used to identify the damage degree by taking the evaluation index of damage degree through the nonlinear damage indicators under harmonic response as a precondition.The damage identification result shows that the method can accurately determine the damage location and quantify the degree of damage to the fatigue fracture,which provides a new effective way for the nonlinear damage assessment.Finally,compared with the traditional BP neural network,the particle swarm optimization support vector regression model has higher recognition accuracy.