Dynamical System Representation and Analysis of Unsteady Flow and Fluid-Structure Interactions

A dynamical system approach is utilized to reduce the representation order of unsteady fluid flows and fluid-structure interaction systems. This approach allows for significant reduction in the computational cost of their numerical simulations, implementation of optimization and control methodologies and assessment of their dynamic stability. In the first chapter, I present a new Lagrangian function to derive the equations of motion of unsteady point vortices. This representation is a reconciliation between Newtonian and Lagrangian mechanics yielding a new approach to model the dynamics of these vortices. In the second chapter, I investigate the flutter of a helicopter rotor blade using finite-state time approximation of the unsteady aerodynamics. The analysis showed a new stability region that could not be determined under the assumption of a quasi-steady flow. In the third chapter, I implement the unsteady vortex lattice method to quantify the effects of tail flexibility on the propulsive efficiency of a fish. I determine that flexibility enhances the propulsion. In the fourth chapter, I consider the stability of a flapping micro air vehicle and use different approaches to design the transition from hovering to forward flight. I determine that first order averaging is not suitable and that time periodic dynamics are required for the controller to achieve this transition. In the fifth chapter, I derive a mathematical model for the free motion of a two-body planar system representing a fish under the action of coupled dynamics and hydrodynamics loads. I conclude that the psicform fish family are inherently stable under certain conditions that depend on the location of the center of mass.