报告摘要：
输液管道广泛应用于核电、冶金、石化等工业领域。输液管道过度振动造成的管道破坏是厂站停工的主要原因之一，在地震环境下尤为显著。本报告运用广义积分变换法分析了输液管道的振动特性，并给出了最新的研究成果。报告首先给出通用弹性边界条件下输液管道的动力学的数学模型，然后讨论四阶Sturm-Liouville特征值问题，以此为广义积分变换提供基函数。区别于传统的双曲函数形式，用指数函数形式表达了各种边界条件组合下Euler-Bernoulli梁的特征函数，以克服高阶特征函数带来的数值求解困难。该广义积分变换的通用步骤适用于各种输液管道的动力学分析。报告最后给出了输送单相流体及气夜两相流的水平管及海洋立管的动力学分析结果，简要介绍广义积分变换在其他结构力学问题中的应用，并展望了流体输送管动力学分析研究的发展前景。
Pipes transporting fluids are widely encountered in industrial applications. Excessive vibration of fluid-conveying pipes is a major cause of equipment failure and plant shutdown， especially under seismic conditions. This talk will present some recent results of dynamical analysis of fluid-conveying pipes with generalized integral transforms. The mathematical models for the dynamics of fluid-conveying pipes are presented firstly, with classical and general elastic boundary conditions. Fourth-order Sturm-Liouville eigenvalue problems are discussed to provide the base functions for generalized integral transforms. Eigenfunctions for Euler-Bernoulli beams with several combinations of end conditions are given in exponential function forms, instead of the traditional hyperbolic function forms, to overcome numerical difficulties associated with high-order eigenfunctions. The formalism of generalized integral transforms is presented and then applied in the dynamical analysis of fluid-conveying pipes. Numerical results are shown for clamped-clamped pipes conveying single-phase fluid and two-phase gas-liquid flow, and marine risers and pipelines conveying gas-liquid two-phase flow. Applications of generalized integral transforms in other structural mechanics problems are briefly reviewed. Finally, the future perspectives of dynamical analysis of fluid-conveying pipes are discussed.
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