A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshotsisused to obtainlow-rank,reduced-rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain.Theapproximationsarethenusedtoobtainabalancedreducedorder model. The method is particularly effective when a small number of outputs is of interest. It is demonstrated for a linearized high-order system that models unsteady motion of a two-dimensional airfoil. Computation of the exact grammians would be impractical for such a large system. For this problem, very accurate reducedorder models are obtained that capture the required dynamics with just three states. The new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition. Although further development is necessary, the concept also extends to nonlinear systems.

/pdf/balanced-model-reduction-via-the-proper-orthogonal-5c77iwc45j.pdf

Balanced Model Reduction via the Proper Orthogonal Decomposition

Introduction to Ordinary Differential Equations * Linear Systems and Stability of Nonlinear Systems * Applications * Hyperbolic Theory * Continuation of Periodic Solutions * Homoclinic Orbits, Melnikov?s Method, and Chaos * Averaging * Local Bifurcation * References * Index.

http://www.math.ecnu.edu.cn/~zmwang/teaching/Advanced_ODE-2014-2015/1-Textbook_and_Reference_book/2-Ordinary%20Differential%20Equations%20with%20Applications.pdf

Ordinary Differential Equations with Applications

https://ntrs.nasa.gov/api/citations/20010018414/downloads/20010018414.pdf

Reduced-order modeling: new approaches for computational physics

Static Aeroelasticity.- Dynamic Aeroelasticity.- Nonsteady Aerodynamics of Lifting and Non-Lifting Surfaces.- Stall Flutter.- Aeroelasticity in Civil Engineering.- Aeroelastic Response of Rotorcraft.- Aeroelasticity in Turbomachines.- Modeling of Fluid-Structure Interaction.- Experimental Aeroelasticity.- Nonlinear Aeroelasticity.- Aeroelastic Control.- Modern Analysis for Complex and Nonlinear Unsteady Flows in Turbomachinery.

/pdf/a-modern-course-in-aeroelasticity-1g3bp11i0h.pdf

A Modern Course in Aeroelasticity

Keywords: aeroelasticite ; structure : dynamique Reference Record created on 2005-11-18, modified on 2016-08-08

/pdf/introduction-to-structural-dynamics-and-aeroelasticity-43ce9fxz1b.pdf

Introduction to Structural Dynamics and Aeroelasticity

Keywords: aeroelasticite ; instationnaire ; structures Reference Record created on 2005-11-18, modified on 2016-08-08

H. Ashley

Papers

Principles of aeroelasticity