Analysis and computation of nonlinear dynamic response of a two-degree-of-freedom system and its application in aeroelasticity

This paper investigates the dynamic response of a coupled two-degree-of-freedom system with a cubic stiffness nonlinearity in both degrees of freedom. The mathematical model is based on a coupled system of Duffing's equations. The governing equations are derived for a two-dimensional airfoil oscillating in pitch and in plunge, but they can be applied to nonaeronautical problems, such as mechanical systems, by discarding the aerodynamics terms and setting the appropriate parameters to correspond to those for the particular dynamic system under consideration. Only the harmonic solution is considered and we use the method of slowly varying amplitude to investigate the dynamic response of the system to an external excitation. The equilibrium points are computed and a linear analysis is carried out to determine the stability of the equilibrium points. Examples are given for a dynamic system without aerodynamic forces to illustrate the complex structure of the jump phenomenon where the solution jumps from one branch of the amplitude-frequency curve to the other. An example in aeroelasticity is given which shows the behaviour of the airfoil motion as the velocity approaches the linear flutter speed. Numerical simulations are also carried out to verify the analytical results. (C) 1997 Academic Press Limited.