This work presents a numerical method for the analysis of fully nonlinear aeroelastic problems. The aeroelastic model consisted of a Navier-Stokes flow solver, a nonlinear structural model, and a solution methodology that assured synchronous interaction between the nonlinear structure and the fluid flow. The flow around the deforming wing was modeled as unsteady, compressible and viscous using the Reynolds-averaged Navier-Stokes (RANS) equations. To reduce the computational time, a three-level multigrid algorithm was implemented and the flow solver was parallelized. The message-passing interface (MPI) standard libraries were used for the parallel interprocessor communication. The computational domain was divided into topologically identical layers that spanned from the root to past the tip of the wing. A novel mesh deformation algorithm was developed to deform the mesh as the structure of the wing was being displaced. The mesh deformation algorithm was able to handle wing tip deformations of up to 60 % of the wing semi-span. Besides being robust, the mesh deforming algorithm was computationally more efficient than regriding, since deforming an existing mesh was computationally less expensive than generating a new mesh for each wing position. Results are presented for the validation and verification of both the flow solver and the aeroelastic solver. The flow solver was validated using: (1) the flow over a flat plate, to validate the turbulent model implementation, and (2) the flow over the NACA 0012 airfoil and over the F-5 wing, to validate the implementation of the convective and viscous fluxes, the time integration algorithm, and the boundary conditions. The aeroelastic solver was validated using: (1) the unsteady F-5 wing undergoing forced pitch motion, and (2) the Nonlinear Aeroelastic Test Apparatus (NATA) wing. In addition, aeroelastic results were generated for the Goland wing. The aeroelastic solver developed herein allows the analysis of aeroelastic phenomena using a fully nonlinear approach. Limit cycle oscillations, which are highly nonlinear phenomena, were captured by the nonlinearities of the flow solver and the structural solver. The impact of the nonlinearities was assessed for the Goland wing, where nonlinear terms changed dramatically the aeroelastic behavior of the wing.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 74-79). Also available via the Internet.

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Missile bodies and wings are typical examples of structures that can be represented by beam models. Such structures, loaded by follower forces along with aerodynamics, exhibit the vehicle's aeroelastic instabilities. The current research integrates a nonlinear beam dynamics and unsteady aerodynamics to conduct aeroelastic studies of missile bodies and wings subjected to follower forces. The structural formulations are based on a geometrically-exact, mixed finite element method. Slender-body theory and thin-airfoil theory are used for the missile aerodynamics, and two-dimensional finite-state unsteady aerodynamics is used for wing aerodynamics. The aeroelastic analyses are performed using time-marching scheme for the missile body stability, and eigenvalue analysis for the wing flutter, respectively. Results from the time-marching formulation agree with published results for dynamic stability and show the development of limit cycle oscillations for disturbed flight near and above the critical thrust. Parametric studies of the aeroelastic behavior of specific flexible missile configurations are presented, including effects of flexibility on stability, limit-cycle amplitudes, and missile loads. The results do yield a significant interaction between the thrust, which is a follower force, and the aeroelastic stability. Parametric studies based on the eigenvalue analysis for the wing flutter, show that the predicted stability boundaries are very sensitive to the ratio of bending stiffness to torsional stiffness. The effect of thrust can be either stabilizing or destabilizing, depending on the value of this parameter. An assessment whether or not the magnitude of thrust needed to influence the flutter speed is practical is made for one configuration. The flutter speed is shown to change by 11% for this specific wing configuration.

The nonlinear dynamic analysis of aeroelastic systems is a topic that has been covered extensively in the literature. The two main sources of nonlinearities in such systems, structural and aerodynamic nonlinearities, have analyzed numerically, analytically and experimentally. In this research project, the aerodynamic nonlinearity arising from the stall behavior of an airfoil is analyzed. Experimental data was used to fit a piecewise linear curve to describe the lift versus angle of attack behavior for a NACA 0012 2 DOF airfoil. The piecewise linear system equilibrium points are found and their stability analyzed. Bifurcations of the equilibrium points are analyzed and applying continuation software the bifurcation diagrams of the system are shown. Border collision and rapid/Hopf bifurcations are the two main bifurcations of the system equilibrium points. Chaotic behavior represented in the intermittent route to chaos was also observed and shown as part of the system dynamic analysis. Finally, sets of initial conditions associated with the system behavior are defined. Numerical simulations are used to show those sets, their subsets and their behavior with respect to the system dynamics. Poincaré sections are produced for both the periodic and the chaotic solutions of the system. The proposed piecewise linear model introduced some interesting dynamics for such systems. The introduction of the border collision bifurcation and the existence of periodic and chaotic solutions for the system are some examples. The model also enables the understanding of the mapping of initial conditions as it defines clear boundaries with different dynamics that can be used as Poincaré sections to understand further the global system dynamics. One of the constraints of the system is its validity as it is dependent on the range of the experimental data used to generate the model. This can be addressed by adding more linear pieces to the system to cover a wider range of the dynamics.

This research explores the impact of kinematic structural nonlinearities on the dynamics of a highly deformable cantilevered wing. Two different theoretical formulations are presented and analysed for nonlinear behavior. The first formulation, which is more conventional, assumes zero equilibrias and structural nonlinearities occur as terms up to third order in the Taylor series expansion of structural nonlinearities. In the second approach, no prior assumption about equilibria states of the wing is made. Kinematic nonlinearities due to curvature and inertia were retained in their exact form. Thus, the former becomes a special case of the latter. This nonlinear formulation permits the analysis of dynamics about nonzero trims. Nonzero trim states are computed as a system parameter is varied using a continuation software tool. The stability characteristics of these trim states are also ascertained. Various bifurcation points of the system are determined. Limit-cycle oscillations are also investigated for and are characterized in terms of amplitude of vibration. The research in particular examines the impact of in-plane degree of freedom on the stability of nonzero trim states. The effect of variation of system parameters such as stiffness ratio, aspect ratio and root angle of attack is also studied. The method of direct eigenanalysis of nonzero equilibria is novel and new for an aeroelastic system.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 100-108).

Thesis (M.S.)--University of Wyoming, 2008. / Title from PDF title page (viewed on July 14, 2009). Includes bibliographical references (p. 43).

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