Skip to main content
main-content
Top

About this book

This self-contained book provides an introduction to the flow-oscillator modeling of vortex-induced bluff-body oscillations. One of the great challenges in engineering science also happens to be one of engineering design – the modeling, analysis and design of vibrating structures driven by fluid motion.
The literature on fluid–structure interaction is vast, and it can be said to comprise a large fraction of all papers published in the mechanical sciences. This book focuses on the vortex-induced oscillations of an immersed body, since, although the importance of the subject has long been known, it is only during the past fifty years that there have been concerted efforts to analytically model the general behavior of the coupling between vortex shedding and structural oscillations. At the same time, experimentalists have been gathering data on such interactions in order to help define the various regimes of behavior. This data is critical to our understanding and to those who develop analytical models, as can be seen in this book. The fundamental bases for the modeling developed in this book are the variational principles of analytical dynamics, in particular Hamilton’s principle and Jourdain’s principle, considered great intellectual achievements on par with Newton’s laws of motion. Variational principles have been applied in numerous disciplines, including dynamics, optics and quantum mechanics. Here, we apply variational principles to the development of a framework for the modeling of flow-oscillator models of vortex-induced oscillations.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
This chapter introduces the focus problem of this monograph, vortex-induced oscillations, which is within the fluid–structure interaction class of problems. The organization of the monograph is provided.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 2. Literature in Vortex-Induced Oscillations

Abstract
A literature review is provided in this chapter of vortex-induced oscillations. While the literature is vast, our review is selective but representative of the field. Reviewed are: (i) experimental studies on: fluid forces, three-dimensionality and free-surface effects, vortex-shedding modes and synchronization regions, frequency dependence of the added mass, the dynamics of cylinders with low mass-damping; (ii) semi-empirical models: wake-oscillator, single degree-of-freedom, force decomposition; (iii) variational approaches; and (iv) numerical approaches.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 3. Introduction to Analytical Mechanics

Abstract
This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrange’s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamilton’s principle , an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrange’s equation. Hamilton’s principle is, especially, relevant to the work in Chaps. 4 and 5.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 4. Variational Models in Fluid Mechanics

Abstract
This chapter introduces a novel approach to the use of variational mechanics in the modeling of fluid mechanics. That is, Hamilton’s principle is used in conjunction with Reynolds transport theorem by McIver in a control volume framework for structures containing fluid. We continue by extending McIver’s ideas to structures that are surrounded by an incompressible fluid. Simple problems are given as example applications.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 5. Lagrangian Flow-Oscillator Models

Abstract
This chapter extends the development of the previous chapter by applying Hamilton’s extended principle to a fluid surrounding a rigid structure. The energies are derived, and the control volume is examined in detail. Boundary conditions are derived and studied. 2D flows past a circular cylinder that is free to move transversely are formulated, and applied to reduced-order modeling. The derived general governing equations for the structure and the flow oscillator are compared with certain published models: Krenk and Nielsen, Hall, Berger, and Tamura and Matsui. It is concluded that the general formulation of this chapter is a good framework for the development of flow-oscillator models of vortex-induced oscillations.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 6. Eulerian and Lagrangian Descriptions

Abstract
This chapter derives the relations between Eulerian and Lagrangian descriptions of displacement and velocity fields, relations between the time derivatives of system properties, variations, and introduces Jourdain’s variational principle. Jourdain’s principle is then applied to viscous incompressible fluids, and the derivation of the energy rate equation. These equations will be utilized in the subsequent chapter for the derivation of the flow-oscillator model for vortex-induced vibration.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 7. Eulerian Flow-Oscillator Models

Abstract
We apply the Eulerian formulations of the last chapter to derive a general variational formulation of a flow-oscillator modeling framework. A brief review of the application of variational principles to fluid–structure interactions is given. A summary is provided of Jourdain’s principle for fluid systems. Boundary conditions are discussed, in particular the no-slip condition and its interpretations. The control volume is expanded upon. Fluid–structure interaction is then modeled in two ways: (i) as a single governing equation of motion for a translating cylinder and for an inverted pendulum, and (ii) as coupled equations of motion utilizing the concept of a wake oscillator. For the wake oscillator, the no-slip condition is further examined and implemented. Experimental data is used to derive a more specific reduced-order model that can be compared with some of the models found in the literature: McIver, Benaroya and Wei, and Hartlen and Currie. A primary conclusion is that the derived framework is an excellent basis for the development of flow-oscillator models, where assumptions are explicitly identified.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Chapter 8. Concluding Thoughts

Abstract
The problem of fluid–structure interaction (FSI) has long been one of the great challenges in engineering. It is a crucial consideration in the design of many engineering systems such as offshore structures, skyscrapers, aircraft, and bridges. This monograph has focused on incompressible flows and bluff bodies. There is also a vast literature and research effort on compressible flows over aerodynamic bodies.
Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Backmatter

Additional information

Premium Partner

    Image Credits