A Study of the Nonlinear Dynamics of a Flap-Lag Rotor Model in Forward Flight

Abstract

For the purposes of stability analyses, it is necessary to describe the dynamic equilibrium state of a rotor blade in forward flight in terms of a Fourier series. Typically, this is assumed to consist of constant and sinusoidal terms that are integer multiples of the rotor speed. Such an approach neglects potentially important dynamics associated with subsynchronous, supersynchronous, and aperiodic responses. The current work investigates the occurrence of such behavior and discusses some conditions where it may be important. Simulation studies are conducted using a simplified nonlinear rotor blade model in forward flight. This model consists of a rigid blade with effective hinges at the root to simulate a hingeless rotor blade. Quasi-steady linear strip theory is used to provide aerodynamic forcing in the model. The nonlinear terms arise from geometrical effects in the structural and aerodynamic modeling procedure. The resulting system of equations is studied using direct numerical integration and harmonic balancing. Nonsynchronous and aperiodic responses are observed for several realistic parameter configurations.