Similitude laws for the structural response of flat plates under a turbulent boundary layer excitation Francesco Franco a,⇑ , Olivier Robin b , Elena Ciappi c , Sergio De Rosa a , Alain Berry b , Giuseppe Petrone a a Pasta-lab, Department of Industrial Engineering, Universitá degli Studi di Napoli ‘‘Federico II”, Via Claudio 21, 80125 Napoli, Italy b Groupe d’Acoustique de l’Université de Sherbrooke (GAUS), Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada c CNR-INSEAN, Italian National Maritime Research Centre, Via di Vallerano, 139, 00128 Roma, Italy article info Article history: Received 17 September 2018 Received in revised form 26 February 2019 Accepted 23 April 2019 Keywords: Similitude laws Flat plates Stochastic structural response Turbulent boundary layer load abstract Similitude laws for scaling the vibration response of flat panels to a turbulent boundary layer excitation are proposed and analyzed in this paper. Their relevance is studied from an analytical, experimental and numerical perspective. It is first shown that a perfect simil- itude, in terms of vibration response scaling, can theoretically be achieved between plates of proportional sides and of variable thicknesses. Vibration auto-spectral and cross-spectral density functions, measured in a wind-tunnel facility on a set of three plates, are then suc- cessfully scaled: the plates dimensions and test flow speeds are a priori defined using the proposed similitude laws. Finally, the applicability of the suggested strategy for different boundary conditions, for different types of materials and properties and for distorted mod- els is also numerically studied and confirmed. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Many engineering problems are solved in a transformed solution domain because the analytical, numerical or experimen- tal analysis can be carried out more easily. These domains or configurations are ruled by specific similitude or analogy laws. Different methodological approaches concerning mechanical systems can be found [1–3]; a well-known example being the mechanical-electrical analogy between some usual mechanical functions like impedance or mobility and equivalent electri- cal circuits. Three review papers [4–6] well highlight the large scientific effort that has been devoted to deal with similitude laws. These reviews present scaling problems of vibrations, but also of kinematics, structural impacts and buckling of structures. In structural mechanics and fluid-dynamics, among all possible frameworks, the solution domain can be geometrically scaled up and down and the active forces are also transformed according to specific similitude laws. In order to predict, by scaling, the induced-vibration or the noise radiated from a structure submitted to an external perturbation, the excitation, the structure and, then, the transmitted vibration or the structural noise have all to be put in similitude, i.e. scaled following adequately defined laws. This paper follows this specific way for transforming the solution domain and the whole engineer- ing problem. In structural dynamics, the first relevant contribution to solve this problem is probably reported in [7], in https://doi.org/10.1016/j.ymssp.2019.04.045 0888-3270/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: francesco.franco@unina.it (F. Franco), olivier.robin@usherbrooke.ca (O. Robin), elena.ciappi@cnr.it (E. Ciappi), sergio.derosa@unina.it (S. De Rosa), alain.berry@usherbrooke.ca (A. Berry), giuseppe.petrone@unina.it (G. Petrone). Mechanical Systems and Signal Processing 129 (2019) 590–613 Contents lists available at ScienceDirect Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp