Hamilton’s Principle for Fluid-Structure Interaction and Applications to Reduced-Order Modeling

2005 ◽  
Author(s):  
Rene D. Gabbai ◽  
Haym Benaroya
Keyword(s):  
General Framework ◽  
Model Problem ◽  
Viscous Flows ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Hamilton’S Principle ◽  
Governing Equations ◽  
Hamilton's Principle ◽  
Reduced Order ◽  
Structure Interaction

A general framework based on the extended Hamilton’s principle for external viscous flows is presented. The indicated method is shown to yield the correct governing equations and boundary conditions when applied to the problem (herein called the “model problem”) of vortex-induced oscillations of an elastically-mounted rigid circular cylinder with a transverse degree-of-freedom. The vortex shedding is assumed to be sufficiently correlated along the span of the cylinder that the flow can be taken as nominally two-dimensional. The incoming flow is assumed to be incompressible, steady, and uniform. The continuity equation results directly from the global mass balance law, thus avoiding its introduction via a Lagrange multiplier. The true strength of this framework lies in the fact that it represents a physically sound basis from which reduced-order models can be obtained. Some preliminary work on this reduced-order modeling applied to the model problem is described.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

Modelling vortex-induced fluid–structure interaction

2007 ◽  
Vol 366 (1868) ◽  
pp. 1231-1274 ◽  
Author(s):  
Haym Benaroya ◽  
Rene D Gabbai
Keyword(s):  
Variational Approach ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Oscillator Model ◽  
List Type ◽  
Governing Equations ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Oscillator Models

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid–structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid–structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion. Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid–structure interaction models entails formulating generalized equations of motion, as a superset of the flow-oscillator models; and developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier–Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

scholarly journals ‘Uncertainty’ principle in two fluid–mechanics

2020 ◽  
Vol 69 ◽  
pp. 47-55
Author(s):  
Sergey Gavrilyuk
Keyword(s):  
Potential Energy ◽  
Second Law Of Thermodynamics ◽  
Coupled System ◽  
Degree Of Freedom ◽  
Hamilton’S Principle ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Hamilton's Principle ◽  
Stationary Action ◽  
Energy Equations

Hamilton’s principle (or principle of stationary action) is one of the basic modelling tools in finite-degree-of-freedom mechanics. It states that the reversible motion of mechanical systems is completely determined by the corresponding Lagrangian which is the difference between kinetic and potential energy of our system. The governing equations are the Euler-Lagrange equations for Hamil- ton’s action. Hamilton’s principle can be naturally extended to both one-velocity and multi-velocity continuum mechanics (infinite-degree-of-freedom systems). In particular, the motion of multi–velocity continuum is described by a coupled system of ‘Newton’s laws’ (Euler-Lagrange equations) for each component. The introduction of dissipative terms compatible with the second law of thermodynamics and a natural restriction on the behaviour of potential energy (convexity) allows us to derive physically reasonable and mathematically well posed governing equations. I will consider a simplest example of two-velocity fluids where one of the phases is incompressible (for example, flow of dusty air, or flow of compressible bubbles in an incompressible fluid). A very surprising fact is that one can obtain different governing equations from the same Lagrangian. Different types of the governing equations are due to the choice of independent variables and the corresponding virtual motions. Even if the total momentum and total energy equations are the same, the equations for individual components differ from each other by the presence or absence of gyroscopic forces (also called ‘lift’ forces). These forces have no influence on the hyperbolicity of the governing equations, but can drastically change the distribution of density and velocity of components. To the best of my knowledge, such an uncertainty in obtaining the governing equations of multi- phase flows has never been the subject of discussion in a ‘multi-fluid’ community.

scholarly journals Reduced-order models for vertical human-structure interaction

2016 ◽  
Vol 744 ◽  
pp. 012030 ◽  
Author(s):  
Katrien Van Nimmen ◽  
Geert Lombaert ◽  
Guido De Roeck ◽  
Peter Van den Broeck
Keyword(s):  
Reduced Order Models ◽  
Reduced Order ◽  
Structure Interaction
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