Summary
Previous research on parametric vibration of pipes has primarily focused on straight configurations. This paper investigates the nonlinear parametric resonance characteristics of slightly curved pipes. Approximate analytical solutions for instability boundary and amplitude-frequency response of pipe parametric resonance are derived. Analytical solutions exhibit excellent agreement with numerical solutions. The mechanism of transition from hardening characteristics to softening of pipes with initial curvature is analyzed for the first time. Then the condition for linear response characteristics is defined by achieving a balance between the square nonlinearity and the cubic. The results show that both natural frequencies and instability boundaries increase as the initial curved amplitude grows. Moreover, modes exchange results in the interchange of instability boundaries in the parametric vibration. The transformation between softening and hardening characteristics of the response under the second-order mode is a unique phenomenon of parametric vibration. Notably, the response intensifies significantly when the parametric vibration of the pipe reaches an intermediate linear state. Finally, the influence of pipe length, outer diameter, and wall thickness on the critical initial curved amplitude that maximizes the response are explored. The research results provide a reference for the rational design of the size of offshore pipes to avoid excessive vibration.
