One of the most important concepts used in the writing of the aeroelastic equations is the generalized aerodynamic force matrix. This entity contains information on the aerodynamic model. However, its definition is based on energy methods used for structural analysis, such as Lagrange’s equations. This chapter introduces the necessary background to later derive the generalized aerodynamic force matrix. In particular, the following topics are introduced:
Virtual displacements and virtual work.
Hamilton’s principle.
Lagrange’s equations and generalized forces.
Exact and approximate transformations between sets of generalized coordinates.
The reader should be aware that these topics are typically introduced in what is termed structural dynamics. The applied forces are not necessarily aerodynamic forces in the presentation of the material of this chapter. However, this book will only use aerodynamic forces to build an aeroelastic stability problem.
Virtual Displacements, Hamilton’s Principle, and Lagrange’s Equations
Introduction to Unsteady Aerodynamics and Dynamic Aeroelasticity ; Kapitel : 22 ; 349-383
11.06.2024
35 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Virtual displacements , Virtual work , Non-conservative forces , Variational operator , Strain energy , Hamilton’s principle , Kinetic energy , Lagrange’s equations , Generalized coordinates , Equations of motion , Damping Engineering , Aerospace Technology and Astronautics , Mechanical Engineering , Mechanical Statics and Structures , Structural Materials , Physics and Astronomy
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