Model reduction for parametric instability analysis in shells conveying fluid
TL;DR: In this article, a model reduction technique is developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure, where only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible.
Abstract: Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection.
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TL;DR: In this paper, the authors present an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants.
Abstract: This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.
188 citations
TL;DR: In this paper, a bibliographical review of finite element methods applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view is given.
Abstract: The paper gives a bibliographical review of finite element methods(FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping—a bibliography [1–3] . The listings at the end of the paper contain 856 references to papers and conference proceedings on the subject that were published in 2001–2004. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; fluid–structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special finite elements for pressure vessels and pipes; finite element software; and other topics.
78 citations
TL;DR: In this article, a finite element formulation for the fully coupled dynamic equations of motion to include the effect of fluid-structure interaction (FSI) is introduced and applied to a pipeline system used in nuclear reactors.
Abstract: Pipes used for transporting high velocity pressurized fluids often operate under time-varying conditions due to pump and valve operations. This can cause vibration problems. In the present work, a finite element formulation for the fully coupled dynamic equations of motion to include the effect of fluid–structure interaction (FSI) is introduced and applied to a pipeline system used in nuclear reactors. The fluid finite element model is based on flow velocity as the variable. The response of fluid filled pipelines to valve closure excitation has been studied. The model is validated with an experimental pipeline system.
67 citations
TL;DR: In this paper, the theoretical and finite element formulations of piezoelectric composite shells of revolution filled with compressible fluid are presented, and various modal results are presented in order to validate and illustrate the efficiency of the proposed fluid-structure finite element formulation.
Abstract: This paper presents the theoretical and finite element formulations of piezoelectric composite shells of revolution filled with compressible fluid. The originality of this work lies (i) in the development of a variational formulation for the fully coupled fluid/piezoelectric structure system, and (ii) in the finite element implementation of an inexpensive and accurate axisymmetric adaptive laminated conical shell element. Various modal results are presented in order to validate and illustrate the efficiency of the proposed fluid–structure finite element formulation.
25 citations
01 Jan 1977
TL;DR: In this article, two efficient numerical methods for dealing with the stability of linear periodic systems are presented, which combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period.
Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet–Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
24 citations
References
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Book•
25 Feb 2014
TL;DR: In this article, the first volume of the Fluid-Structure Interaction (FSI) series, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid.
Abstract: The first of two books concentrating on the dynamics of slender bodies within or containing axial flow, Fluid-Structure Interaction, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes. In this edition, Chapter 7 from Volume 2 has also been moved to Volume 1, meaning that Volume 1 now mainly treats the dynamics of systems subjected to internal flow, whereas in Volume 2 the axial flow is in most cases external to the flow or annular. * Provides an in-depth review of an extensive range of fluid-structure interaction topics, with detailed real-world examples and thorough referencing throughout for additional detail. * Organized by structure and problem type, allowing you to dip into the sections that are relevant to the particular problem you are facing, with numerous appendices containing the equations relevant to specific problems. * Supports development of long-term solutions by focusing on the fundamentals and mechanisms needed to understand underlying causes and operating conditions under which apparent solutions might not prove effective.
1,175 citations
TL;DR: In this paper, the dynamics and stability of flexible pipes containing flowing fluid are examined in a general way and it is shown that conservative systems are subject not only to buckling (divergence) at sufficiently high flow velocities, but also to oscillatory instabilities (flutter) at higher flow velocity.
Abstract: This paper deals with the dynamics and stability of flexible pipes containing flowing fluid, where the flow velocity is either entirely constant, or with a small harmonic component superposed. An extensive historical review of the subject is given. In the case of constant flow velocity, the dynamics of the system is examined in a general way and it is shown that conservative systems are subject not only to buckling (divergence) at sufficiently high flow velocities, but also to oscillatory instabilities (flutter) at higher flow velocities. Also presented are some new results for cases of systems subjected to internal dissipative forces. In the case of harmonically varying flow velocity, the equation, of motion derived here exposes an error in a previous derivation. Stability, maps are presented for parametric instabilities, computed by Bolotin's method, for pipes with pined or clamped ends, as well as for cantilevered pipes. It is found that the extent of the instability regions increases with flow velocity for clamped-clamped and pinned-pinned pipes, while a more complex behaviour obtaines in the case of cantilevered pipes. In all cases, dissipation reduces the extent of, or entirely eliminates, parametric instability zones.
518 citations
TL;DR: In this article, a review of the dynamics of pipes conveying fluid is presented, with a focus on the nonlinear and chaotic dynamics of pipe conveying systems, and a selective review of recent work on this problem is presented.
Abstract: This paper reviews the dynamics of pipes conveying fluid and presents a selective review of the research undertaken on it. It is endeavoured to show that this system is fast becoming a new paradigm in dynamics, on a par with, for instance, the classical problem of the column subjected to compressive loading, but one capable of displaying much richer dynamical behaviour. The dynamics of pipes with supported ends, cantilevered pipes or with unusual boundary conditions; continuously flexible pipes or articulated ones; pipe conveying incompressible or compressible fluid, with steady or unsteady flow velocity; pipes thin enough to be treated as thin shells; linear, nonlinear and chaotic dynamics; these and many more are some of the aspects of the problem considered. An Appendix is provided for those unfamiliar with the modern methods of nonlinear analysis.
419 citations
"Model reduction for parametric inst..." refers background in this paper
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...ıdoussis and Li [5] a detailed description of almost all types of problems related to pipes conveying fluid is discussed....
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Book•
01 Dec 1987
TL;DR: In this article, the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow was analyzed and applications of analytical methods and experimental data in design evaluation of various system components.
Abstract: This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders.
345 citations
"Model reduction for parametric inst..." refers background in this paper
...[3,5,25]....
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...Chen’s [3] book on flow-induced vibration presented a detailed investigation of the flowinduced vibration of cylindrical structures, while Pa....
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...ıdoussis and Issid [1], Ginsberg [2], Chen [3] and Pa....
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TL;DR: In this paper, two efficient numerical methods for dealing with the stability of linear periodic systems are presented, which combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period.
Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
269 citations