Crack Recognition Method Of Beam Structure Based On Geometric Characteristics Of Phase Diagram

From the beginning of human development and manufacturing of engineering structure,there are always a series of structural damage problems around.The current production technology level cannot completely guarantee that the structures are completely free of cracks.With the increase of structural complexity and the influence of many factors such as materials,environment and long-term service,the structure is extremely vulnerable to different degrees of crack damage,and even lead to fatigue fracture accidents,threatening the safety of people’s lives and properties.Therefore,it is of great significance to take effective technical measures to study and promote the identification technology of structural cracks for improving the safety and reliability of engineering equipment and predicting the maximum service life of components.In this paper,theoretical and numerical methods are used to analyse the dynamic characteristics of the sandwich beam with and without skin breathing cracks,and research the dynamic characteristics of the cantilever beam with breathing cracks.By comparing the influence of different crack parameters on the vibration parameters of the beam,a crack identification method based on the geometric characteristics of the phase diagram is proposed by combining with the contour line method.The main contents of this paper are as follows:The Zig-Zag theory is used to describe the geometric deformation of the skin and core of lattice sandwich beam,the nonlinear dynamic equation of simply supported pyramid lattice sandwich beam under transversal excitation is derived based on Hamilton principle and Galerkin method.The model with breathing crack is equivalent to a single degree of freedom nonlinear spring vibrator model,and then the additional flexibility is introduced into the nonlinear dynamic equation of the normal sandwich beam to obtain the dynamic equation of the sandwich beam with breathing crack.The areas of phase diagrams are calculated by pixel method,and the relative variation of the areas of phase diagrams of the sandwich beam with cracks is described by quasi standard deviation that we defined.Under the excitation condition of the same main resonance frequency,the variation of geometric characteristics of the phase diagram with the crack parameters is analyzed.The feasibility and rationality of the method are verified by numerical simulations.In order to make the above recognition method more universal,the research on identification of cantileverwith breathing crack based on phase diagram geometric features was carried out.The influence of crack parameters on phase diagram geometry of cantilever beam with periodic change breathing crack is analyzed by studying phase diagram geometry characteristics of cantilever beam with periodic change breathing crack in the first mode of single-degree-of-freedom system.Under the condition of main resonance frequency excitation and superharmonic resonance frequency excitation,several crack identification indexes are defined,and the influence of crack parameters on each index is analyzed.The contour line parameters of each identification index were used to identify crack parameters,and the feasibility and effectiveness of the method are verified by the numerical example.Considering the breathing effect of the crack,the local stiffness at the crack location is assumed to be a non-linear function of the amplitude.Combined with the stiffness model and the dynamic equation of the elastic beam,the multimode natural frequency expression of the cantilever beam with breathing crack is derived.The multi-modal dynamic differential equation of the cantilever beam is established by discretizing the beam.On this basis,the effects of crack parameters on the natural frequency and phase diagram geometry of the cantilever are studied.Finally,the phase diagram area obtained from the first three orders excited by the superharmonic resonance frequency is taken as three indexes to identify the crack parameters,and the influence of the crack parameters on the identification indexes is analyzed.