A wavenumber analysis of the coupling of a structural mode and flow turbulence

A Wavenumber Approach to Modelling the Response of a Randomly Excited Panel, Part I: General Theory

“…Equation (25) is a classical expression that has been used by many authors to evaluate the response of a #uid-loaded plate to a turbulent wall-pressure [23, 24, 27}31]. However, recent advances in the modelling of turbulence have provided expressions for the wall-pressure #uctuations given in the form of a wavevector}frequency power spectrum [7,14] and an increasing number of studies are now considering formulations in the wavenumber}frequency domain [11,13,32,33].…”

Hydrodynamic and hydroelastic analyses of a plate excited by the turbulent boundary layer

“…It is clear that most of the energy of WPF is concentrated around the convective peak and then any correlation data is mainly the representation of the convective character of the TBL. Unfortunately, only few experimental data concerning direct measurements of the wavenumber-frequency spectrum are available (Abraham, 1998;Choi and Moin, 1990;Panton and Robert, 1994;Farabee and Geib, 1991;Manoha, 1996) and, among them, a big spread of the spectra magnitude at low wavenumbers is present as reported for example by Hwang and Maidanik (1990).…”

Vibrations of plates with clamped and free edges excited by low-speed turbulent boundary layer flow

“…Also, approximate forcing function models that represent only the surface interaction, or low-wavenumber TBL forcing function content (for the fully clamped plate) and the edge interaction, or convective wavenumber TBL forcing function content (for the plate with a free edge) were evaluated using the analyses. Hwang and Maidanik's (1990) assertion that free edged structures accept significant energy at convective wavenumbers even at low U c =c m ratios appears to be correct. Also, the approximate edge force spectrum presented appears to provide reasonable accuracy for U c =c m ratios > 0:1 for lightly damped structures.…”

“…3, the plate flexural response is very sensitive to its boundary conditions (Hwang and Maidanik, 1990). Using analyses of the wall pressures and plate response in wavenumber space, Hwang and Maidanik found that the response of plates with clamped and simply supported edges excited by slow moving TBL flow was due almost entirely to acceptance of wall pressure energy in the low-wavenumber region, or surface interaction.…”

“…The edge force depends on the pressure levels and spatial coherence near the convective ridge ðU c =c m B1Þ and the shape of the excited mode at the plate edge. The force/length spectrum acting on a free edge normal to the flow (either upstream or downstream of the flow) may be approximated using methods from Hwang and Maidanik (1990) as…”