Exact and numerical responses of a plate under a turbulent boundary layer excitation

The aim of this paper is the analysis of the predictive capabilities of the deterministic methodologies when facing the problem of a plate excited by a stochastic pressure distribution due to a turbulent boundary layer (TBL). A full analytical solution has been assembled by considering a simply supported rectangular plate wetted on one side by a TBL. This reference exact solution, developed by using a standard separable variable model, has been used as test case for comparing the approximate solutions coming from the adoption of a numerical scheme by using discrete coordinates. The numerical algorithm has been built by using a standard finite element modal approach. The approximations introduced are thoroughly discussed and analysed; they refer to the meshing condition and the transformation of the distributed stochastic load. The application of a novel numerical procedure named as Asymptotical Scaled Modal Analysis is presented too. This innovative numerical scheme allows the analysis of the structural response of a generic plane operator in the whole frequency range, which is not always amenable by exact solutions; further and equally important, it is associated to a reduction of the computational cost. The work demonstrates that some numerical advances in the prediction of the random structural responses are feasible still using standard finite element modal inputs, without increasing the computational costs.