Mathematical models for understanding phenomena: Vortex‐induced vibrations

Abstract

This is a rather biased review paper emphasizing the importance of "understanding" of phenomena. This paper's purpose is to inspire young researchers to taste the real charms of research by observing the process of development of mathematical models of vortex-induced vibration phenomena of cylinders for understanding their essential mechanism. It first discusses the limitations of human abilities and important aspects of research. Then, it emphasizes the close relation between understanding and mathematical models, and five conditions for a desirable mathematical model: simplicity; inclusion of all essential properties; possession of physical meanings; wide scope of application; and possibility of development. It refers to Birkhoff's wake-oscillator (1953), Funakawa's early-wake model (1969), Nakamura's 2DOF flutter model (1970), the Hartlen-Currie model (1970), the Iwan-Blevins model (1974), Tamura's non-linear wake-oscillator model with a variable length (1979), and the Tamura-Shimada model (1987) for combined effects of vortex resonance and galloping. Some recent developments of the Tamura-Shimada model are also introduced. Then, it discusses the necessity of accurate experimental capture of early-wake behavior and the aerodynamic properties of a target cylinder in a given flow condition for further development of Tamura's model and the Tamura-Shimada model. Finally, the necessity for efforts to understand phenomena are emphasized. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Experimental study on unsteady aerodynamics of an oscillating three-dimensional prism in uniform and turbulent boundary layer flows using forced vibration technique

“…Overall, the trends observed in both the test and predicted values align well, consistent with previous studies (Marukawa et al, 1996;Quan et al, 2005). Steckley and Vickery (1989;1993), Cooper et al (1997), Song (2015) and Chen et al (2021bChen et al ( , 2020aChen et al ( , 2018Chen et al ( , 2017 and conform to the vibration laws of the Van der Pol oscillator model (Tamura, 2020). Moreover, the above results also demonstrate the self-excited and limiting-amplitude characteristics of vortex-induced vibration (Guo et al, 2022(Guo et al, , 2021: when the across-wind vibration amplitude is small, the aerodynamic damping ratio can compensate for a greater portion of the structural damping ratio, thereby augmenting the wind-induced response.…”

Stochastic diffusion characterises early colony formation in Mediterranean coral Corallium rubrum

“…See[52] for an excellent take on the role of modelling in describing natural phenomena 2. The book is a part of a series that includes similar considerations on sea shells[58] and plants[59].…”

Modelling of Flow-Induced Vibration of Bluff Bodies: A Comprehensive Survey and Future Prospects

“…In addition to the "lock-in" phenomenon, VIV also exhibits various forms of stronger non-linear oscillatory behavior. These include resonance delay (where the amplitude of vibration reaches its maximum at a velocity greater than the resonance velocity U R ≡ f n D/S t where S t is the Strouhal number and D is a characteristic length of the structure), hysteresis (producing different amplitude responses as the flow speed is increased or decreased), and a multi-valued response (where a given fixed velocity can result in multiple values for the vibration amplitude) [11]. The dynamical characteristics of lock-in makes VIV an ideal choice for fluid energy harvesting.…”

“…The success of this modelling approach depends critically on an accurate and deep intuitive understanding of the physics underlying FIV phenomena. This is the key to formulating a good theoretical model that meets the following conditions [11]: (i) simplicity of formulation; (ii) inclusion of all essential (important) characteristics of the underlying physical phenomena; (iii) utilization of concepts and quantities of interest that are physically meaningful (interpretable and explainable); (iv) capability to provide accurate and universal predictions; (v) wide applicability especially to complex cases; and (vi) possibility for model to be further developed and generalized. It should be noted that frequently the terminology of mathematical modelling as it relates to FIV concerns the theoretical analysis of the phenomenon and, in this context, it is also referred as a theoretical or analytical model.…”