{"title":"Linear and Nonlinear Development of Bending Perturbations in a Fluid-Conveying Pipe with Variable Elastic Properties","authors":"","doi":"10.1134/s0081543823040028","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> We consider bending vibrations of a fluid-conveying pipe resting on an elastic foundation with nonuniform elasticity coefficient. Previously A. G. Kulikovskii showed analytically that the elasticity parameters can be distributed in such a way that at every point the system is either locally stable or convectively unstable. In this case, despite the absence of local absolute instability, there exists a global growing mode whose formation is associated with the points of internal reflection of waves. In the present paper, we perform a numerical simulation of the development of the initial perturbation in such a system. In the linear formulation we demonstrate how the perturbation is transformed into a growing eigenmode after a series of reflections and passages through a region of local instability. In the nonlinear formulation, where the nonlinear tension of the pipe is taken into account within the von Kármán model, we show that the perturbation growth is limited; in this case the vibrations acquire a quasi-chaotic character but do not leave the region bounded by the internal reflection points determined by the linearized problem. </p> </span>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823040028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider bending vibrations of a fluid-conveying pipe resting on an elastic foundation with nonuniform elasticity coefficient. Previously A. G. Kulikovskii showed analytically that the elasticity parameters can be distributed in such a way that at every point the system is either locally stable or convectively unstable. In this case, despite the absence of local absolute instability, there exists a global growing mode whose formation is associated with the points of internal reflection of waves. In the present paper, we perform a numerical simulation of the development of the initial perturbation in such a system. In the linear formulation we demonstrate how the perturbation is transformed into a growing eigenmode after a series of reflections and passages through a region of local instability. In the nonlinear formulation, where the nonlinear tension of the pipe is taken into account within the von Kármán model, we show that the perturbation growth is limited; in this case the vibrations acquire a quasi-chaotic character but do not leave the region bounded by the internal reflection points determined by the linearized problem.
摘要 我们考虑的是位于弹性系数不均匀的弹性地基上的流体输送管的弯曲振动问题。此前，A. G. Kulikovskii 通过分析表明，弹性参数的分布方式可以使系统在每一点上要么局部稳定，要么对流不稳定。在这种情况下，尽管不存在局部绝对不稳定性，但存在一种全局增长模式，其形成与波的内部反射点有关。在本文中，我们对这种系统中初始扰动的发展进行了数值模拟。在线性模型中，我们演示了扰动如何在经过一系列反射和穿过局部不稳定区域后转化为增长特征模。在非线性公式中，管道的非线性张力在 von Kármán 模型中被考虑在内，我们证明扰动的增长是有限的；在这种情况下，振动具有准混沌特性，但不会离开由线性化问题确定的内部反射点所限定的区域。
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