Research On The Identification Method Of Crack Parameter For Cantilever Beams By Natural Frequency

Cantilever beam is a kind of basic component which is widely used in many fields such as aeronautics and astronautics, mechanical engineering, civil construction and energy chemical industry. During of working time, it is unavoidable for the beam elements to endure vibration so that it is easy to produce crack damage, even fatigue crack. Therefore, it is very important for the cracked cantilever beam to study the crack identification technology so as to improve it’s the safe reliability to engineering equipment. In this paper, the cantilever beam is employed as the study object to propose a kind of crack detecting technology by resonance frequency based on the contour line method and the impact mechanisms of crack parameters on the resonance frequency of cantilever beams. The main works that were done includes:Firstly, the impact mechanisms of crack parameters on resonance of cantilever beam were studied. During analysis, one cracked beam was simplified into two elastic continuums medium beams that were connected by a nonlinear torsion spring. Combined with fracture mechanics and energy principle, the local flexible formula of cracked beam was derived. One quadratic polynomial equation stiffness model was set up under the hypothesis that the stiffness of the cantilever beam is a nonlinear function of vibration amplitude with the breathing effect of crack during of vibration involved. Coupled with stiffness model and dynamical model of elastic beam, the resonance frequency equation was obtained for the breathing cracked cantilever beam. Thereafter, case studies were done to find the influence law of crack location, crack depth and vibration amplitude on resonance frequency of cantilever beam. The study results provide one kind of theoretical model of crack identification for the cantilever beam.Then, a crack parameter identification method of a cracked beam was proposed by combing the contour line method and the resonance frequency equation. In this method, response surface of resonance for cracked cantilever beam based on the first three modal frequencies at first. Take the first three specified resonance frequency value to construct a plane and intersect with frequency response surface at the same time to get the same contour line. The transvers coordinate of intersect point of the contour line will denote the location of the crack. To verify the effective of this method, the analytical resonance frequency and the experimental resonance frequency were used as the input source to do case study. Results indicate that the method of crack identification by contour line is very helpful. But the identification precision depends on the precision of experiment resonance frequency.A new crack identification method for cracked cantilever beam by harmonic response curve was proposed in the end with the insensitivity of crack parameters on resonance frequency. Many different FEM model of cantilever beam with different crack was studied by Abaqus software during analysis. The amplitude and frequency scope of external force was determined by the modal analysis of non-crack cantilever beam. And the frequency response of the cantilever beam that corresponding to different crack condition was obtained by harmonic analysis. Results indicate that the location and the amplitude of response will be changed with the change of crack parameters. So it is feasibility to complete crack identification by harmonic response analysis for cantilever beam.