Vibration Analysis Of Inherent Characteristics And Responses For A Nonuniform Graded Beam With Multiple Breathing Cracks

As a new type of material,non-uniform functionally graded materials can be designed to achieve the advanced target by changing the composition ratio of the material.Since the concept was put forward,it has attracted high attention of the researchers in the area of science materials.During the process of structure vibration,the cross section of breathing cracks is not always separate,but alternately vary by the pattern of "open-closure".In this paper,the vibration problem of simply supported beam of non-uniform functionally gradient material with single breathing crack and multiple breathing cracks is studied by the means of quantitative calculation and CAE simulation.In the static part,choose the triangular element which is degenerated to mesh the structure at the crack tip.The simulation results are compared with the stress intensity factor obtained by the self-compiled program,and the formula of the stress intensity factor about the crack depth ratio is fitted.In the modal part,using the local flexibility method,work out the local flexibility coefficient based on the fitting formula.The modal functions for the simply supported beam are solved and carry on a deep analysis for the vibration characteristics of the structure.By comparison with the transfer matrix method and the experimental results,it has a certain precision.In the vibration part,based on the Lagrange equation and modal superposition method,the time domain response of the cracked functionally graded material simply supported beam is obtained,and its frequency response is obtained by the FFT transform.According to the calculating results,the vibration responses of the structure under different conditions can be obtained.