Introduction to Nonlinear Aeroelasticity

4Determining the Vibration Parameters

4.1 Introduction

The previous chapter detailed a number of methods for calculating numerically the response of nonlinear aeroelastic systems. All response types can be calculated using these approaches, including oscillatory, non‐oscillatory, periodic and aperiodic. However, numerical solutions do not give the same amount of information as analytic solutions. For example, the exact solution of the linear systems in Section 2.3 calculates not only the complete trajectory from any set of initial conditions but also the frequency and amplitude of oscillation if the response is oscillatory. This kind of information is not directly available from a numerical solution or from experimental measurements. Furthermore, nonlinear system solutions are more complex than linear ones, since the frequency can vary in time, the responses can be Limit Cycle Oscillations or chaotic and they are dependent on initial conditions.

This chapter will introduce a number of techniques for estimating the properties of response data from nonlinear aeroelastic systems, experimental or numerical. These properties concern mainly the instantaneous frequency and amplitude, as well as the stability of the responses. The methodologies will rely on signal processing and nonlinear dynamics approaches. Some of them will be applied to numerical data after the response has been calculated. Other techniques need to be implemented in the time integration scheme for best results. ...