Prediction of the response of a thin structure subjected to a turbulent boundary-layer-induced random pressure field

A method capable of predicting the root mean square displacement response of a thin structure subjected to a turbulent boundary-layer-induced random pressure field is presented. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular elements with six degrees of freedom per node. The displacement functions are derived from thin shell theory. Description of the turbulent pressure field is based on the Corcos formulation for cross spectral density of pressure fluctuations. A numerical approach is proposed to obtain the total root mean square displacements of the structure. Exact integration over surface and frequency leads to an expression for the response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a thin plate under different boundary conditions subjected to a turbulent boundary layer were calculated and illustrated as a function of free stream velocity and damping ratio and the effects of flow direction on the response were also investigated. In addition, the power spectral densities of the displacements of an SFSF plate subjected to a fully developed turbulent flow were studied. The total root mean square radial displacement of a thin cylindrical shell was obtained and compared favorably with that in the literature.