Flexural vibration behavior of a cracked straight pipeline, divided into two complete pipelines which were jointed together with a massless torsion spring simulating the outer surface circumferential crack, was analyzed with the Laplasse transform method and the transfer matrix theory, based on a straight pipeline FSI transverse vibration 4-equation model. At the same time, the equivalent spring method was also applied to simulate the elastic supports at both ends of the cracked straight pipeline, assuming that the pipeline was symmetrically supported and there were a line spring and a torsion spring at each end. The transverse vibration matrix equations model without or with frequency domain excitation force were finally obtained and then the natural frequencies were solved with Matlab. The natural frequency calculated results were compared with those of the finite element method to verify the correctness of the analysis process, and at last the influences of elastic support coefficient, crack angle, depth and location on the dynamic behaviors of the cracked straight pipeline were calculated and discussed.

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