Introduction to Nonlinear Aeroelasticity

Abstract

Introduction Nonlinear aeroelasticity is the study of the interactions between inertial, elastic and aerodynamic forces on engineering structures that are exposed to an airflow and feature non-negligible nonlinearity. There exist several good textbooks on linear aeroelasticity for aircraft (Bisplinghoff et al. 1996; Fung 1993; Hodges and Alvin Pierce 2002; Wright and Cooper 2015). Dowell (2004) even includes chapters on nonlinear aeroelasticity and stall flutter, while Paidoussis et al. (2011) discusses a number of nonlinear aeroelastic phenomena occurring in civil engineering structures. However, there is no introductory text that presents the methodologies of nonlinear dynamics and applies them to a wide range of nonlinear aeroelastic systems. The present book aims to fill this gap to a certain degree. The subject area is vast and mutlidisciplinary and it would be impossible to fit every aspect of it in a textbook. The main omission is high fidelity numerical simulation using Computational Fluid Dynamics and Computational Structural Dynamics solvers; these methodologies are already the subject of a dedicated text (Bazilevs et al. 2013). The aerodynamic models used in this book are analytical, empirical or based on panel methods while the structural models are either analytical or make use of series solutions. The book is introductory but it assumes knowledge of structural dynamics, aerodynamics and some linear aeroelasticity. The main linear aeroelastic phenomena of flutter and static divergence are discussed in detail because they can affect nonlinear behaviour, but the present work is by no means a complete text on linear aeroelasticity. Unsteady aerodynamic modelling is used throughout the book and discussed in Chapters 8, 10 and in the Appendix. However, again this book is not a complete reference on unsteady aerodynamics, linear or nonlinear. On the other hand, nonlinear dynamics and bifurcation analysis are presented in great detail as they do not normally feature in most undergraduate or even graduate Aerospace and Mechanical Engineering courses. The emphasis of all discussions is on the application rather than the rigorous derivation of the theorems; there already exist several classic textbooks for the latter (Kuznetsov 1998; Guckenheimer and Holmes 1983). More application-based works on nonlinear dynamics also exist (e.g. Strogatz 1994) but they address a wide range of physical, chemical, biological, accounting models, to name a few, whereas the present book concentrates exclusively on aeroelastic phenomena.

Nonlinear System Identification of an All Movable Fin with Rotational Freeplay by Subspace-Based Method

“…Because of the existence of freeplay, the nonlinear vibrating system has discontinuous nonlinear stiffness and becomes three piecewise linear systems with different regions. For nonlinear systems with freeplay, the nominal system is the overlying linear system (OLS), that is the system without freeplay (d = 0 as shown in Figure 2a) and full stiffness [37]. Moreover, the underlying linear system (ULS) possessing zero stiffness (k o = 0 in Figure 2a) on the source of freeplay is also important for the nonlinear mechanical system.…”

Designing a Control System for an Airplane Wing Flutter Employing Gas Actuators

“…In quasi-steady aerodynamic forces, the simplest, possible modeling includes ignoring the effects of the wake. From the thin airfoil theory for the lift coefficient, the following equation is obtained [2]:…”

“…From the thin airfoil theory for moment and lift coefficients and (9), the following equations are obtained [2]:…”

“…Flutter is a result of interaction of aerodynamic, inertial, and elastic forces as is shown in Figure 1; discussion and investigation of the phenomenon are related to the field of aeroelasticity [1,2]. Such an event can occur in somewhat flexible structures, such as airplane wings, telegraph wires, bridges, and buildings [3].…”

Isolated resonances and nonlinear damping

“…DiBerardino and Dankowicz [24] identified IRCs related to symmetry breaking in a two-DoF system; adopting isola singularity identification, in combination with a multiple scale approach, they managed to predict the outbreak of an IRC. In [25], an IRC related to an internal resonance was encountered, while in [26] the phenomenon was explained through a frequency gap due to phase locking.Isolated branches of periodic solutions can also be related to self-excited oscillations [27][28][29][30]. Apart from mechanical systems, this is a typical and well-studied phenomenon in chemical reactors [31][32][33][34], but also in biological models [35,36].…”