New Improved g Method for Flutter Solution

Abstract

T HE field of aircraft engineering is entering an era of high technology. Over the past decade there has been a great deal of progress in almost all the subfields in aeronautics. However, in the aeroelastic field, despite the complexity of coupling three distinct engineering disciplines, aerodynamics, structures, and dynamics into a unified aeroelastic analysis capability, computational aeroelasticity has enjoyed a significant number of successes over its course of development. Today, every manned vehicle that flies through our atmosphere undergoes some level of aeroelastic analysis before flight. Also every major unmanned flight vehicle is similarly analyzed. Furthermore, flutter is a catastrophic aeroelastic phenomenon that must be avoided at all costs, and all flight vehicles must be clear of flutter and many other aeroelastic phenomena in their flight envelope. Flight and wind tunnel testing are two ways to clear a vehicle for flutter, but both are expensive and occur late in the design process. Therefore, engineers rely heavily on computational methods to assess the aeroelastic characteristics of flight vehicles. The successes of computational aeroelasticity are rooted in this aeroelastic characterization process. Traditionally flutter calculations in frequency domain are performed using either theKmethod or theP-Kmethod. TheKmethod is generally very fast and quite simple, but it has a downfall in that sometimes the frequency and damping values “loop” around themselves and yield multivalue frequency and damping as a function of velocity. TheKmethod solution is only valid when g 0 (g refers to damping) and the structural motion is neutrally stable and matches the aerodynamic motion which is also neutrally stable. The P-K method is acknowledged to provide more accurate modal damping values than the K method. Gradually, the P-K method has become the most widely used method in aeroelastic engineering. In recent years, a g method was proposed by P. C. Chen, who uses the analytic property of unsteady aerodynamics and a damping perturbation approach. Although these two methods of P-K method and g method are different in the equation form, they share the same stability criterion, i.e., eigenroot of aeroelastic equation is solved and a root with positive real part indicates flutter. In addition, the g method uses a reduced-frequency sweep technique to search for the roots of the flutter solution and a predictorcorrector scheme to ensure the robustness of the sweep technique. This g method includes a first-order damping term in the flutter equation that is rigorously derived from the Laplace-domain aerodynamics. In the paper, however, the improved g method increases a second-order damping term in the flutter equation. It is also valid in the entire reduced frequency domain and up to the second order of damping.