A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System

Q2 Physics and Astronomy Advances in Acoustics and Vibration Pub Date : 2017-01-01 DOI:10.1155/2017/8141523
V. Olunloyo, C. Osheku, P. Olayiwola
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引用次数: 6

Abstract

This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work) as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system’s natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.
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不可压缩流体输送管道系统解析解的注释
本文给出了考虑陀螺力或科里奥利力作用的流体输送管段方程的积分变换解析解。该数学模型将管道的一段理想化为输送不可压缩流体的弹性梁。很清楚地表明,当这样的系统两端都有支撑并且处于自由运动时,科里奥利力不会耗散能量(或者根本不起作用),因为它对所有流速产生共轭复杂振动分量。证明了由复频率对的代数积可以计算出模态固有频率。显然,当绘制实分量和虚分量时,可以部分地看到系统固有频率的特征模式,这在文献中广泛可见。尽管如此,本研究的结果表明,当绘制任何速度的绝对值时,存在连接亚临界、临界和后临界振动行为的连续性剖面。与此同时,通过证实早期工作者(如Paidoussis, Ziegler等)的预测和结果的有效性,证明了该方法对通常假设的空间或时间模态解决方案的有效性和多功能性,其中展示了发散前和后的行为。
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期刊介绍: The aim of Advances in Acoustics and Vibration is to act as a platform for dissemination of innovative and original research and development work in the area of acoustics and vibration. The target audience of the journal comprises both researchers and practitioners. Articles with innovative works of theoretical and/or experimental nature with research and/or application focus can be considered for publication in the journal. Articles submitted for publication in Advances in Acoustics and Vibration must neither have been published previously nor be under consideration elsewhere. Subject areas include (but are not limited to): Active, semi-active, passive and combined active-passive noise and vibration control Acoustic signal processing Aero-acoustics and aviation noise Architectural acoustics Audio acoustics, mechanisms of human hearing, musical acoustics Community and environmental acoustics and vibration Computational acoustics, numerical techniques Condition monitoring, health diagnostics, vibration testing, non-destructive testing Human response to sound and vibration, Occupational noise exposure and control Industrial, machinery, transportation noise and vibration Low, mid, and high frequency noise and vibration Materials for noise and vibration control Measurement and actuation techniques, sensors, actuators Modal analysis, statistical energy analysis, wavelet analysis, inverse methods Non-linear acoustics and vibration Sound and vibration sources, source localisation, sound propagation Underwater and ship acoustics Vibro-acoustics and shock.
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