Study of Nonlinear Stiffness and Damping Effects on Shimmy and Flutter

Abstract

This work deals with the fundamentally similar dynamic behavior of two apparently different aircraft systems, namely, landing gears and all-movable control surfaces. Both systems typically contain stiffness and damping nonlinearities, leading to shimmy/flutter limit cycle oscillations (LCOs). In a series of earlier papers the authors have developed highly efficient computational methods, based on describing functions, to construct LCO responses for dynamic systems with concentrated nonlinearities in stiffness or damping. These methods are extended in the present paper, and the focus is on the physical insights that can be obtained by using them for systems with multiple nonlinearities. The model parameters are varied to obtain an array of interesting results. For example, each branch of the landing gear response is attributable to a particular nonlinearity. Based on this, a possible reason is advanced for the occurrence of shimmy in the F/A-18 aircraft. On the other hand, the entire flutter response of the all-movable surface can be viewed as being shaped by one nonlinearity and modified by the other. Finally, the well-known Wright Air Development Center wind tunnel flutter test results for an all-movable horizontal tail with freeplay are reinterpreted and explained in the light of the present findings.