Fatigue life analysis of a slightly curved hydraulic pipe based on Pairs theory

As key components of a hydraulic system, fatigue failure caused by unwanted vibrations is a common failure type for hydraulic pipes. As ideal straight pipes are inexistent in engineering, the fatigue life of slightly curved pipes is an issue worth discussing. The purpose of this paper is to analyze the influence of initial curved shape and flow velocity on fatigue life of hydraulic pipe under harmful vibration. Firstly, governing equation of the slightly curved pipe is established by the generalized Hamilton’s principle. The nonlinear partial differential integral equation is discretized to a set of nonlinearly coupled ordinary differential equations (ODEs) by the Galerkin method. The harmonic balance method (HBM) is used to solve these ODEs. Compared with the numerical solution by differential quadrature element method (DQEM), the accuracy of HBM is verified. On the basis of this verification, effects of the initial curve, the excitation and the flow velocity on the distribution of tensile stress, bending stress and resultant stress are analyzed by HBM. Then, the fatigue life of the pipe is predicted based on Pairs theory. The analysis results show that, as the initial curved shape enhances the bending stiffness of the pipe, it improves the fatigue life of the pipe. On the contrast, the fluid velocity decreases the bending stiffness and it reduces the fatigue life of the pipe correspondingly. Bigger excitation is also harmful to the fatigue life as it arouses more drastic vibration. These conclusions provide more reliable theories for designing safe and reliable hydraulic pipe systems and other pipes conveying fluids.