Amjad Tuffaha

On well-posedness for a free boundary fluid-structure model

We address a fluid-structure interaction model describing the motion of an elastic body immersed in an incompressible fluid. We establish a priori estimates for the local existence of solutions for a class of initial data which also guarantees uniqueness.

Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface

We address the system of fluid–structure interaction consisting of a compressible Navier–Stokes equation coupled with an elasticity equation, with the velocity and stress continuity requirements across the free moving interface. We prove the a priori estimates for existence of solutions when the initial velocity belongs to H 3 , the initial density is bounded from below and belongs to H 3/2+r , where r> 0, and the initial velocity of the displacement is in H 3/2+r .

On well-posedness and small data global existence for an interface damped free boundary fluid–structure model

We address a fluid?structure system which consists of the incompressible Navier?Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

Strong solutions to a Navier–Stokes–Lamé system on a domain with a non-flat boundary

In this paper, we consider a Navier?Stokes?Lam? system modeling a fluid?structure interaction. For a general domain, we establish local well-posedness for strong solutions in which initial velocity u0 belongs to H1 while the initial data (w0, w1) for the elasticity equation belongs to (H3/2+k, H1/2+k) for any k (0, k0) where k0 is an explicit positive constant.

Boundary feedback control in Fluid-Structure Interactions

We consider a boundary control system for a fluid structure interaction model. This system describes the motion of an elastic structure inside a viscous fluid with interaction taking place at the boundary of the structure, and with the possibility of controlling the dynamics from this boundary. Our aim is to construct a real time feedback control based on a solution to a Riccati equation. The difficulty of the problem under study is due to the unboundedness of the control action, which is typical in boundary control problems. However, this class of unbounded control systems, due to its physical relevance, has attracted a lot of attention in recent literature (cf. [5], [18], [11]). It is known that Riccati feedback (unbounded) controls may develop strong singularities which destroy the well-posedness of Riccati equations. This makes computational implementations problematic, to say the least. However, as shown recently, this pathology does not happen for certain classes of unbounded control systems usually referred to as singular estimate control systems (SECS) (cf. [11], [21]). For such systems, there is a full and optimal Riccati theory in place, which leads to the well-posedness of feedback dynamics. Our objective is to show that the boundary control problem in question falls in the class of singular estimate control systems (SECS). Once this is accomplished, an application of the theory in [21] leads to the main result of this paper which is well-posedness of Riccati equations and of the Riccati feedback synthesis.

The Stochastic LQR Optimal Control with Fractional Brownian Motion

We consider the stochastic linear quadratic optimal control problem where the state equation is given by a stochastic differential equation of the Ito–Skorokhod type with respect to fractional Brownian motion. The dynamics are driven by strongly continuous semigroups and the cost functional is quadratic. We use the fractional isometry mapping defined between the space of square integrable stochastic processes with respect to fractional Gaussian white noise measure and the space of integrable stochastic processes with respect to the classical Gaussian white noise measure. By this mapping we transform the fractional state equation to a state equation with Brownian motion. Applying the chaos expansion approach, we can solve the optimal control problem with respect to a state equation with the standard Brownian motion. We recover the solution of the original problem by the inverse of the fractional isometry mapping. Finally, we consider a general form of the state equation related to the Gaussian colored noise, we study the control problem, a system with an algebraic constraint and a particular example involving generalized operators from the Malliavin calculus.

The Stochastic Linear Quadratic Control Problem with Singular Estimates

We study an infinite dimensional finite horizon stochastic linear quadratic control problem in an abstract setting. We assume that the dynamics of the problem are generated by a strongly continuous semigroup, while the control operator is unbounded and the multiplicative noise operators for the state and the control are bounded. We prove an optimal feedback synthesis along with well posedness of the Riccati equation for the finite horizon case. Our results extend the ones proposed in [C. Hafizoglu, Ph.D. Thesis, University of Virginia, Charlottesville, VA, 2006.] to the case in which disturbance in the control is considered and a final time penalization term is included in the quadratic cost functional.

Flutter analysis of an articulated high aspect ratio wing in subsonic airflow

We present a methodology for calculating flutter speeds of a high aspect ratio flying wing articulated with point masses in inviscid air flow. This highly flexible wing configuration typically models a HALE (High Altitude Long Endurance) UAV (Unmanned Aerial Vehicle) type aircraft. To demonstrate the procedure, we perform flutter analysis on an actual articulated wing model and we investigate the dependence of the flutter speed on the number of loads mounted onto the structure and the number of panels comprising the flying wing for both varying and constant span. The results show that the flutter speed decreases as more panels and point masses are incorporated into the flying wing. On the other hand, the number of point masses mounted onto the structure has a small effect on the flutter speed if the wing span is kept constant.

The transonic dip in aeroelastic divergence speed—An explicit formula

Abstract Using continuum models we develop a closed form analytical formula for the divergence speed as a function of the Mach number and in particular its dependence on wing camber. There is a transonic dip even when the angle of attack is zero and it depends on the wing thickness ratio. For nonzero camber the angle of attack in fact plays a lesser role. The main analytical tool is the Possio integral equation which is shown to have an explicit solution. Neither CFD nor FEM is employed.

Sharp trace regularity for an anisotropic elasticity system

We establish a sharp regularity result for the normal trace of the solution to the anisotropic linear elasticity system with Dirichlet boundary condition on a Lipschitz domain. Using this result we obtain a new existence result for a fluid-structure interaction model in the case when the structure is an anisotropic elastic body.