Abstract Internal resonance and stress distribution of pipes conveying fluid at the supercritical flow around curves have been firstly investigated, with the goal of improving the mechanical fatigue properties of such pipes. Axial pre-pressure as a way of regulating the onset and growth of 1:3 internal resonance has been examined. Based on the direct multi-scale method and the Galerkin method, an approach has been proposed to analyze the nonlinear gyroscopic elastic system with time-dependent nonlinear perturbations. The tensile, bending, and resultant vibratory stress distributions of the pipe system have been determined in the presence of 1:3 internal resonance. Internal resonance degrading fatigue properties of the pipes has been highlighted. The numerical simulations support the analytical results. Then the analytical frequency responses are employed to identify factors that govern the internal resonance and stress distribution and to offer explanations as to why improving fatigue life is accompanied by suppression in the internal resonance. The boundary for incurring internal resonance suggests that appropriate axial pre-pressure should be modified in the presence of 1:3 internal resonance at different fluid velocities.

中文翻译：

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超临界状态下输送流体管道的内共振与应力分布

摘要 首次研究了超临界曲线下输送流体管道的内共振和应力分布，以提高管道的机械疲劳性能。已经研究了轴向预压作为调节 1:3 内部共振的发生和增长的一种方式。基于直接多尺度法和伽辽金法，提出了一种分析具有瞬态非线性扰动的非线性陀螺弹性系统的方法。管道系统的拉伸、弯曲和合成振动应力分布已在存在 1:3 内部共振的情况下确定。突出了管道的内部共振降解疲劳性能。数值模拟支持分析结果。然后使用解析频率响应来识别控制内部共振和应力分布的因素，并解释为什么提高疲劳寿命伴随着内部共振的抑制。引起内部共振的边界表明，在不同流体速度下存在 1:3 内部共振的情况下，应修改适当的轴向预压。