Earl H. Dowell

TL;DR: In this article, the primary resonance and the 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay were analyzed.

Abstract: We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

TL;DR: In this paper, the equations of motion for aeroelasticity of plates and shells are well established and results obtained by numerical time integration have been compared to those obtained by topological theories of dynamics and also from experiment.

TL;DR: In this article, an aerodynamic model for flutter and limit cycle oscillations (LCO) of two-dimensional elastic plates in three-dimensional axial flow were observed.

TL;DR: In this article, a three-degree-of-freedom aeroelastic model with freeplay is modeled theoretically using a small number of aerodynamic eigenmodes (i.e., a reduced order model) based upon Peters' finite-state model for two-dimensional aerodynamic flow.