Accurate numerical prediction of flutter boundary for fighter aircraft is of great importance. Existing models are deterministic, and do not allow for inherent variations in the system parameters. These variations (e.g. structural dimensions, aerodynamic flow field, stores properties) propagate to uncertainty in the model predictions. In this paper we examine variations in structural dimensions of a "heavy" version of the Goland wing on the flutter boundaries. Initially, the large number of random quantities (component thicknesses and areas) are efficiently reduced by conducting a sensitivity analysis of the baseline wing. Next, an optimization study is carried out to provide a design of the wing that maximizes its first natural frequency while constraining the frequency of the remaining nine modes to no less than their baseline wing counterpart values. The sensitivity study enables selection of a random variable set of the wing components having significant impact on the wing natural frequencies. Monte Carlo simulation is used to propagate the variation in the dimensional properties of the selected set of random quantities of the designed wing. The effect of correlation between random variables is considered. A modal analysis of each realization is evaluated using MSC.Nastran. Flutter boundaries of the propagated sample are predicted based on linear aerodynamic theory (ZAERO R), resulting in a "banded" stability boundary. Results indicate the high sensitivity of the flutter speed to small changes in the structure with an apparent switching in the failure modes.
This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay. The representative problem, known as the delayed damped Mathieu equation, is chosen to illustrate the combined effect of a time delay and parametric excitation on stability. A discrete linear map is obtained by approximating the exact solution with a series expansion of orthogonal polynomials constrained at intermittent nodes. Characteristic multipliers of the map are used to determine the unstable parameter domains. Additionally, the described analysis provides a new approach to extract the Floquet transition matrix of time periodic systems without a delay.
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