Vibration Analysis Of A Functionally Graded Beam With Breathing Crack

Functionally graded material (FGM) is a kind of materials that have specific function by changing the volume fraction of constituents. Since it can be designed, FGM s are widely used in various industrial fields. The breathing crack is the non-linear process of crack plane "open-closed" alternate variations when structure vibrating. Compared with opening crack, breathing crack is more close to the engineering practice.Based on the non-linear model of the breathing crack, the paper analyzes the non-linear vibration problem of non-uniform FGM beam through quantitative calculation In the static parts, this paper uses 8 node elements to establish finite element model of graded material structure with crack and imitates the singularity in crack tip by degenerate elements. The stress intensity factor (SIF) is calculated by writing C++ program based on finite element method, and the synthetic formula is proposed. In the modal section, based on the crack compliance method, this paper obtains piecewise function to determine the modal function of beam with crack by the fitting formula for SIF and analyzes its vibration characteristics deeply. In the vibration section, considering the non-linear both for materials and crack, we have calculated non-linear vibration response of FGM beam in time domain based on modal superposition method and Lagrange equations. Then the frequency response is obtained by FFT. According to the results, the vibration responses of FGM beam with breathing crack are discussed by the different gradient changes, and the changing rule of the crack depth and crack position are also analyzed in detail.