This chapter presents an introduction to numerical continuation and discusses the intricacies of its application to aeroelasticity. Before applying numerical continuation to dynamic systems, the chapter demonstrates the methodology on algebraic problems. The continuation procedure starts with locating a solution to the nonlinear equations, then it estimates a direction vector and subsequently it follows the branch on which the initial solution is located, negotiating folds in the process. Numerical continuation can be used in order to calculate the fixed points. As a case study, the chapter considers the unsteady symmetric pitch‐plunge‐control wing with quadratic damping and cubic stiffness in pitch. Finite differences and shooting are two different techniques for turning the periodic responses of nonlinear aeroelastic systems into algebraic problems that can be solved using numerical continuation. Another such approach is the Harmonic Balance method. The chapter explains the Harmonic Balance method and uses it in a numerical continuation framework.
Numerical Continuation
Introduction to Nonlinear Aeroelasticity ; 313-388
2017-03-28
76 pages
Article/Chapter (Book)
Electronic Resource
English
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