Frequencies and Flutter Speed Estimation for Damaged Aircraft Wing Using Scaled Equivalent Plate Analysis

Abstract

Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.