A fatigue life analysis method for shallow curved hydraulic pipes with unstable alternating stress

Fatigue failure of hydraulic pipes, resulting from unstable alternating stress, is a common type of failure for hydraulic systems. In engineering, the reality of working with perfect straight pipes is nonexistent. Instead, the fatigue life of shallow curved pipes is an essential topic worth careful consideration and discussion. The purpose of this paper is to investigate the effect of dual-frequency excitation on the fatigue life of hydraulic pipes with an initial curved shape exposed to unstable alternating stress. Firstly, the governing equation of the shallow curved pipe is established by the generalized Hamilton principle. Secondly, the nonlinear partial differential integral equation is discretized into a set of nonlinearly coupled ordinary differential equations (ODEs) through Galerkin method. The effectiveness of GM (Galerkin method) is verified using DQEM (Differential quadrature element method). Upon this, the influence of the frequency difference between two frequencies on the forced vibration of the pipe midpoint is discussed. The phenomena of bifurcation and chaos in the transverse vibration of a system near the first natural frequency are analyzed exhaustively. The analysis shows that a low gap of frequency causes chaotic behavior. The Fourier series expansion technique is used to decouple the unstable alternating stress generated when chaos occurs. Based on Pairs theory, the linear combination mechanism of pipe life under decoupling stress is proposed, and the fatigue life of pipe under chaos is predicted. Finally, the potential impact of chaos on pipe fatigue life is investigated. The results of this research project expand the theoretical research field of pipe dynamics, provide effective research methods for a precise understanding of the entire lifecycle of pipe structures, and thus yield valuable insights and guidance for the reliability design, system management, maintenance of pipes, and fault prediction of pipe systems.