Modeling vibrating panels excited by a non-homogeneous turbulent boundary layer

Abstract

Predicting the vibration response of an elastic structure excited by a turbulent flow is of interest for the civil and military transportation sector. The models proposed in the literature are generally based on the assumption that the turbulent boundary layer (noted TBL in the following) exciting the structure is spatially homogeneous. However, this assumption is not always fulfilled in practice, in particular when the excited area is close to the starting point of the TBL or with curved structures. To overcome this issue, this work proposes to extend two approaches generally used for dealing with homogeneous TBL, namely the spatial and the wavenumber approaches. The extension of the spatial approach to non-homogeneous excitation is relatively straightforward and gives us a reference, however with costly computation. On the contrary, extending the wavenumber approach requires more developments and assumptions that have led the authors to develop a sub-area decomposition technique (SDT). It consists in partitioning the excited area in several sub-areas, assuming a homogeneous TBL pressure field on each sub-area and neglecting certain interactions between the sub-areas. A criterion on the sub-area size as a function of the minimum wavelength of the wall pressure field is proposed on the basis of the numerical calculations. A test case on a plate with varying thickness and excited by a growing TBL allows us to highlight: (1) the interest of the SDT compared to a classical calculation considering a homogeneous TBL; (2) the efficiency of the SDT in terms of computing time compared to the spatial approach.