Flutter analysis of aircraft wing using equivalent-plate models with orthogonal polynomials

A method of equivalent simplification, using equivalent-plate models (EPMs), is developed. It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing structures. It is on the assumption that the wing structures discussed are composed of skin, beams and ribs, and the different plate units (such as skin, beam web, rib web) are not distinguished in modeling, which is to avoid the complex pre-processing and make it more generalized. Taking the effect of transverse shear deformation into consideration, the equivalence is based on the first-order shear deformation theory, and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent modeling. The Ritz method is applied with the Legendre polynomials, which is used to define the geometry, structure and displacements of the wing. Particularly, the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the ill-conditions. This is in contrast to the EPM method based on the classical plate theory. Through vibration and flutter analysis, the results obtained by using EPM agree well with those obtained by the finite element method, which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.