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 ; Chapter : 22 ; 349-383
2024-06-11
35 pages
Article/Chapter (Book)
Electronic Resource
English
Variational operator , Non-conservative forces , Hamilton’s principle , Virtual displacements , Generalized coordinates , Damping , Kinetic energy , Lagrange’s equations , Virtual work , Equations of motion , Strain energy Mechanical Engineering , Physics and Astronomy , Structural Materials , Mechanical Statics and Structures , Aerospace Technology and Astronautics , Engineering
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