Calculation of Aeroelastic Limit Cycles due to Localized Nonlinearity and Static Preload

Abstract

The presence of a static preload can significantly alter the limit cycle oscillation response of nonlinear aeroelastic systems. This paper reports a numerical study of two distinct types of preload, mechanical (i.e., independent of flow velocity) and aerodynamic (i.e., dependent on flow velocity), and their effects on limit cycle behavior. Simulations are carried out on models of a wing-with-store and an all-moving surface, respectively, with linear potential flow aerodynamics and a localized structural nonlinearity. Novel, computationally efficient methods based on dual-input describing functions are proposed and employed for calculating limit cycles, thereby generalizing earlier work that used single-input describing functions for the no-preload situation. Results are presented for a smooth nonlinearity (cubic hardening) and a nonsmooth one (classical freeplay), along with selected time marching responses. Finally, the feasibility of including nonlinear aerodynamics in the present framework is discussed.