Recently, pipelines have been extensively applied in engineering transportation because of their excellent continuity and high efficiency. Nevertheless, harmful noise and vibration will be generated in complex engineering application environments. We conducted a comprehensive study on the construction of three-dimensional pipelines for transporting gas–liquid two-phase flow using fiber-reinforced composite materials (FRC). Building upon this foundation, we developed an innovative pipeline configuration incorporating bidirectional nonlinear energy sinks (NES) and implemented parameter optimization techniques to maximize the vibration suppression performance of the system. According to the Euler–Bernoulli beam theory, the three-dimensional governing equations of the pipelines acted by the external excitations were established by adopting Hamilton's variational principle. The ordinary differential equation of the system motion was obtained by discretizing variables utilizing the Galerkin technique. The frequency response characteristics were achieved using the harmonic balance method combined with a pseudo-arc length extension approach. The effects of parameters such as fiber orientation angle, damping coefficient, liquid volume coefficient, liquid velocity, and external excitation amplitude on the frequency responses of the FRC three-dimensional pipe were explored. To ensure the correctness of this analytical method, the present results were contrasted with the response curve obtained by the Runge–Kutta technique. Additionally, the nonlinear dynamic evolution of the pipelines, including the bifurcation and chaos, was further predicted using global bifurcation diagrams incorporated with phase diagrams and Poincaré diagrams, which provided a significant reference for the design of the pipes conveying the two-phase flow. Additionally, this study designed two additional NES attached on the pipeline structure to conduct the three-dimensional vibration control, analyzed their vibration reduction effect, and optimized the control parameters through genetic algorithm to improve their vibration control effect.
Wang et al. (Fri,) studied this question.