Introduction to Nonlinear Aeroelasticity

2Nonlinear Dynamics

2.1 Introduction

This chapter will introduce the subject of nonlinear dynamics and will discuss some of its most important concepts. The analysis will focus on dynamic systems with a single degree of freedom, such as the linear harmonic oscillator and the galloping oscillator. Although the concepts addressed in this chapter can be found in other textbooks on nonlinear dynamics, the context is aeroelastic. Furthermore, the information presented here will be used in later chapters in order to analyse more realistic aeroelastic systems with many degrees of freedom and various nonlinearities.

Some of the important concepts to be discussed are common to both linear and nonlinear dynamical systems. Examples are fixed points, the phase plane, response trajectories and stability. As linear systems have analytical solutions, they will be preferred to nonlinear ones for the introduction of such concepts. The early parts of the chapter are therefore mostly devoted to linear dynamics; readers already familiar with the subject should read these sections as a revision but also as a familiarisation with the terminology that will be encountered throughout the book.

The main part of the chapter concerns nonlinear dynamics. Concepts such as multiple solutions, bifurcations and limit cycle oscillations will be introduced on simple nonlinear systems. The emphasis is not on the calculation of solutions of the equations of motion; such calculations will be presented in the ...