Analytical Representation of Aerodynamic Forces in Laplace Domain

摘要

With the impetus provided by numerical differences between the body-axis solution and the flutter (MFP-axis) solution for the short-period response, the current study was undertaken to gain a better understanding of the aerodynamic force models. The difference in the low-frequency response was inaccurately explained in Ref. 1 as a numerical convergence problem intrinsic to the MFP-axis formulation. Further investigation showed that the discrepancy rather is a consequence of differing aerodynamic force representations in the Laplace domain. In the present Engineering Note, various aerodynamic models, that is, analytical continuations related to the choice of reference system, are described. It is demonstrated how the MFP-axis formulation introduces singularities in the EOM. The singularities are identified, and the effect of their removal is shown in a numerical application. The conclusion is that the body-axis formulation generally leads to a more accurate solution. As part of the current investigation, equations were derived for the steady-state limits of common motion variables. These limits are not affected by the various modeling techniques discussed here.