Investigating Low-Dimensional Representations for Body Freedom Flutter

A hierarchy of low-dimensional models are proposed for accurately predicting a nontraditional aeroelastic instability known as body-freedom-flutter (BFF). This instability arises when rigid-body pitching modes become commensurate with wing bending modes. The goal is to provide an alternative to computationally intensive investigations in order to facilitate fundamental understanding of the aerodynamic and mechanical mechanisms underlying BFF. Lagrange’s equations with generalized forces due to quasi-steady and unsteady aerodynamics are used to derive a minimal but mathematically canonical modeling framework based on the aeroelastic typical section. Models with only two degrees-of-freedom (DOF) are shown to be capable of predicting coalescence between rigid-body rotation with wing bending as freestream velocity increases. The importance of quasi-steady aerodynamics is shown for certain parameter ranges. Next, a four DOF model is developed that augments the two-DOF model with fuselage plunge and wing torsion with a more advanced unsteady aerodynamic model. Comparisons between the two- and four-DOF models are discussed.