Modal forcing functions for structural vibration from turbulent boundary layer flow

In this paper, several approaches for combining large-scale finite-element structural vibration models with turbulent boundary layer (TBL) forcing functions are evaluated. The objective is to determine an efficient method to predict the surface displacement and radiated acoustic power. The overall formulation is based on a standard modal summation approach, and the focus of this work is the calculation of the modal force matrix. Direct numerical integration of the modal force is shown to be very computationally intensive and requires overly resolved structural models. However, an asymptotic approximation to the TBL model provides a very efficient method to compute the modal force at high frequencies. The asymptotic results are equivalent to full numerical integration when the TBL correlation lengths are roughly an order of magnitude smaller than the structural wavelengths. Additionally, the asymptotic solution also removes any dependence of the structural mesh resolution. Analytical formulas using this approach are derived for structures with and without free edges. Example results are shown for a simple isotropic plate and for a complex rib-stiffened plate at low speed in water.