Investigation of an Asymptotic Expansion Technique to Analyze Limit Cycle Response of Aerodynamic Surfaces with Structural Nonlinearities

摘要

Defining the flutter and divergence characteristics of aerodynamic surfaces is a basic requirement in assuring structural and performance integrity of a given design for its operational environment. Divergence and flutter phenomena are unstable motions with increasing amplitude. For systems containing structural nonlinearities, another mode of aeroelastic response limit cycle oscillation may be present. The potential of limit cycle response is important since these oscillations may occur within the aerodynamic surface flutter and divergence flight envelope and may lead to fatigue damage of the system even through aeroelastic instability is not encountered. The objective of this thesis is to evaluate, on a comparative basis, different numerical simulation approaches for predicting limit cycle response of aerodynamic surfaces containing discrete structural nonlinearities. Results from such simulations are needed to compare and evaluate approximate solutions for the limit cycle response of nonlinear systems. In addition, these simulation results provide information concerning the nature of the nonlinear system response which may be used to aid in understanding the mechanism of the aerodynamic surface dynamics and in understanding the response of nonlinear systems in general. The numerical integration techniques selected for evaluation were: fourth-order Runge-Kutta, eighth-order Shanks, and fourth-order Adams-Moulton predictor-corrector. Results of the three simulation techniques compared well with each other. Keywords: Limit cycle oscillation, Structural nonlinearity, Flutter analysis.