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NONLINEAR RESPONSE OF PIPES CONVEYING FLUID WITH A BREATHING CRACK UNDER HARMONIC LOAD
Fengchun Cai, Xianhui Ye, Qian Huang, Wenzheng Zhang

Last modified: 2018-06-25

Abstract


Abstract: In this paper, the formula of local flexibility at crack location in pipes conveying fluid is established. According to the compatibility conditions of displacement, rotation angle, shear force and bending moment and the boundary conditions of the pipes, the mode shape functions of the cracked pipes were established. Then based on the Lagrange’s equation for a system containing non-material volumes, an equation of motion for pinned-pinned pipes conveying fluid with a breathing crack under harmonic load were derived. The equations of motion of the cracked pipe conveying fluid were discretized by the modal functions of cracked pipe, and the discrete equations of motion of the cracked pipe were obtained. The mass matrix, damping matrix, stiffness matrix varied with time due to opening and closing of the crack. Then numerical methods were used to solve the discrete equations and the dynamic response characteristics of the cracked pipe conveying fluid under harmonic excitation load were studied. the superharmonic resonance and sub-harmonic resonance could be shown when the pipes conveying fluid was under harmonic excitation load. In this paper, the influence of system parameters including crack depth, crack location, system damping and flow velocity on the harmonic components in the system response were investigated finally. and a ratio is used to describe the relative magnitude of each harmonic component in the response of cracked pipes conveying fluid. These results could provide a reference for crack identification for cracked pipes conveying fluid.


Keywords


breathing crack; pipes conveying fluid; super-harmonic resonance; sub-harmonic resonance

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