Modelling vortex-induced fluid-structure interaction.

Area of Science:

• * Fluid Dynamics
• * Structural Mechanics
• * Applied Mathematics

Background:

• * Existing models for fluid-structure interactions (FSI) often lack generality.
• * Previous work established a single energy equation for FSI.
• * Flow-oscillator models, comprising coupled oscillators for fluid and structure, are a specific type of FSI model.

Purpose of the Study:

• * To generalize Hamilton's variational framework for deriving physics-based, reduced-order analytical models of nonlinear FSI.
• * To establish a general framework encompassing flow-oscillator models as a subclass.
• * To develop a superset of flow-oscillator models capable of handling multiple degrees of freedom.

Main Methods:

• * Application of Hamilton's principle-based variational approach for reduced-order model development.
• * Generalization of the variational formulation to derive systems of governing equations.
• * Coupling of Navier-Stokes equations with a structural oscillator model.

Main Results:

• * Demonstrated that flow-oscillator models are a subclass of the generalized physical-based framework.
• * Developed a general model shown to be a superset of flow-oscillator models.
• * Established a framework yielding systems of governing equations for multiple degrees of freedom FSI.

Conclusions:

• * The generalized variational approach provides a flexible paradigm for complex, multi-degree-of-freedom FSI problems.
• * Future research requires experimentally derived functions for key terms in the governing equations.
• * The developed framework allows for the derivation of various flow-oscillator models based on different assumptions.