Flow, Turbulence and Combustion 61: 85–99, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. 85 Response of a Thin Cylindrical Shell Excited by a Turbulent Internal Flow PIERRE-OLIVIER MATTEI and PAUL J.T. FILIPPI Laboratoire de Mécanique et d’Acoustique, UPR 7051 CNRS, 31, chemin Joseph-Aiguier, 13042 Marseille Cedex 20, France Abstract. This paper presents results obtained within the scope of a collaboration between the “Laboratoire de Mécanique et d’Acoustique” (Marseille, France), the “Laboratoire de Mécanique des Fluides et d’Acoustique” of the Ecole Centrale (Lyon, France) and the “Laboratoire de Vibra- tions et d’Acoustique” of the Institut National des Sciences Appliquées (Lyon, France). The main aspect of this collaboration is to establish a comparison between a measured and a model vibro- acoustics response of a thin cylindrical pipe excited by a turbulent internal flow. After a brief review of the literature, a model of the response of the shell, based on a matched asymptotic expansion, is given. Some numerical results are also given. The spectral density of the acceleration of the shell is compared with experimental results. Key words: vibro-acoustics, fluid loading interaction, turbulent flow, cylindrical shell. 1. Introduction Turbulent boundary excitation of a structure is a phenomenon of great practical im- portance, particularly in the field of high-speed transport technology. The problem involves the coupling of structural and fluid vibrations. This aspect has assumed increased importance because of the emergence of problems of dense fluid loading in the field of marine acoustics and fluid machinery. Moreover, mass optimisation leads to an increase in the sensibility of a structure to its surrounding fluid and then to the excitation by a wall pressure fluctuation. While many studies have been published on the problem of a thin elastic plate (or membrane) excited by a turbulent boundary layer, little is known about the vibro-acoustic response of a shell. This is mainly because during the last decades the turbulent flow had not been considered as a major source of noise in regards to other phenomena such as vortex shedding, propagating plane waves and acoustic high-order modes inside a pipe or mechanical excitation [18]. Actually, these sources became well understood and the turbulent excitation again became a field of research. To our knowledge, the first attempt to make a realistic comparison of measured and predicted pipe vibration was made by Clinch [5]; the hypotheses made for the theoretical model (continuous resonant response) and the results obtained are valid at high frequencies. But only the first resonance frequencies of the shell make a significant contribution to the