Authors:
Dr. Sheri Martinelli | The Pennsylvania State University | United States
PhD Andrew Wixom | The Pennsylvania State University | United States
PhD Micah Shepherd | The Pennsylvania State University | United States
PhD Stephen Hambric | The Pennsylvania State University | United States
PhD Robert Campbell | The Pennsylvania State University | United States
An understanding of the influence of the fluctuating wall-pressure field beneath a turbulent boundary layer (TBL) is critical in the design of structures subject to fatigue loading or noise radiation (e.g., aircraft, watercraft or automobiles). Many models have been developed to provide a statistical description of this forcing, based mainly on flat plate assumptions augmented by fits to empirical data. One such model, by Corcos [G.M. Corcos / J. Sound. Vib. 6: 59–70, 1967], poses an exponential correlation model that incorporates empirically-derived parameters treated as universal constants. In this work, we expand the process of Corcos in terms of its parameters, which we treat as uncertain, using the technique of Karhunen-Loève. We then incorporate the truncated result into a generalized polynomial chaos (gPC) expansion of the modal response – the solution to the forward model. Given the gPC coefficients for a structure of interest, the resulting representation of the forward model can be used as an efficient means to generate data [Y. Marzouk and D. Xiu / Commun. Comput. Phys. 6(4): 826-847, 2009] in order to estimate the posterior distribution of the unknown parameters. The approach also produces expressions for the structure’s modal response, both eigenvalues and eigenfunctions, in terms of the random variables, permitting the study of the impacts of uncertain forcing on the mode shapes and natural frequencies. Results will be compared to standard estimates which typically assume Gaussian densities on system output.