Introduction to Aircraft Aeroelasticity and Loads

C

Aircraft Symmetric Flexible Modes

In the treatment of manoeuvres and gust encounters in this book, the whole free–free aircraft is considered, initially as a rigid body and then with a single flexible mode added to illustrate the important effect of flexibility. The aim of the flexible mode representation is to keep the mathematics as basic as possible while illustrating the impact that flexibility might have. In particular, the flexible mode shapes described in this appendix are used in Chapters 13 to 17 for manoeuvres (flight and ground) and gust/turbulence encounters; only one flexible mode is used in each case, but its shape is derived from a ‘master’ mode template and may be altered. The mode is first introduced in Chapter 13 but some of the content is repeated here for convenience, with modal parameters being derived. In this appendix, the constituent flexible mode shapes and modal parameters will be introduced in order to avoid significant digressions in the main chapters of the book. The idea is to define the flexible mode shapes geometrically, apply conditions of orthogonality to the rigid body modes and so determine the modal masses for the flexible modes; the modal stiffness may then be found simply by choosing the desired natural frequency. Therefore no modal analysis is performed explicitly.

C.1 AIRCRAFT MODEL

The free–free aircraft is shown in Figure C.1. It has unswept and untapered flexible wings with the mass distributed uniformly along the span and with the ...