Abstract
Similitude laws for the vibration response of simply supported plates under random excitations are derived and tested numerically and experimentally for the case of a turbulent boundary layer. Analytical calculations show that under the assumption of proportional sides, perfect similitude in terms of vibration response scaling can be achieved between plates of variable thicknesses. It is also highlighted that even if the similitude conditions are not all satisfied (i.e., a complete scaling of all the involved parameters, from panel dimensions to flow speed), an approximation can be made in the mid-high-frequency domain that leads to satisfactorily scaled results. Based on the analytical study, a series of tests is performed in an anechoic wind tunnel on three-scaled simply supported panels at different flow velocities. Applying the proposed procedure to this set of vibration measurements leads to satisfactory scaling of results between each other.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Defined by \(k_c=\omega /U_c\) and \(k_b=\big (\frac{\rho \times h \times \omega ^2}{D} \big )^{\frac{1}{4}}\), respectively.
References
Franco, F., De Rosa, S., Ciappi, E.: Numerical approximations on the predictive responses of plates under stochastic and convective loads. J. Fluids Struct. 42, 296–312 (2013)
Ciappi, E., Magionesi, F., De Rosa, S., Franco, F.: Analysis of the scaling laws for the turbulence panel responses. J. Fluids Struct. 32, 90–103 (2012)
Xiaojian, Z., Bangcheng, A., Ziqiang, L., Dun, L.: A scaling procedure for panel vibro-acoustic response induced by turbulent boundary layer. J. Sound Vib. 380, 165–179 (2016)
De Rosa, S., Franco, F., Meruane, V.: Similitudes for the structural response of flexural plates. Proc. IMechE Part C: J. Mech. Eng. Sci. 230(2), 174–188 (2016)
Meruane, V., De Rosa, S., Franco, F.: Numerical and experimental results for the frequency response of plates in similitude. Proc. IMechE Part C: J. Mech. Eng. Sci. 230(18), 3212–3221 (2016)
Corcos, G.M.: Resolution of pressure in turbulence. J. Acoust. Soc. Am. 35, 192–199 (1963)
Bull, M.K.: Wall-pressure fluctuations beneath turbulent boundary layers: some reflections on forty years of research. J. Sound Vib. 190(3), 299–315 (1996)
Miller, T.S., Gallman, J.M., Moeller, M.J.: Review of turbulent boundary layer models for acoustic analysis. In: Proceedings of the 49th AIAA Aerospace Sciences Meeting, 4–7 Jan 2011, Orlando, Florida—AIAA paper 2011-1083 (2011)
Hwang, Y.F., Bonness, W.K., Hambric, S.A.: Comparison of semi-empirical models for turbulent boundary layer wall pressure spectra. J. Sound Vib. 319(1), 199–217 (2009)
Elishakoff, I.: Probabilistic Methods in the Theory of Structures. Wiley, New York (1983)
De Rosa, S., Franco, F.: Exact and numerical responses of a plate under a turbulent boundary layer excitation. J. Fluids Struct. 24, 212–230 (2008)
Blake, W.K.: Mechanics of Flow Induced Sound and Vibration. Academic Press, Orlando (1986)
Farabee, T.M., Casarella, M.J.: Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3, 2410–2420 (1991)
Goody, M.: An experimental investigation of pressure fluctuations in three-dimensional turbulent boundary layers. Ph.D. Thesis, Department of Aerospace and Ocean Engineering, Virginia Tech, USA (1999)
Robin, O., Chazot, J.D., Boulandet, R., Michau, M., Berry, A., Atalla, N.: A plane and thin panel with accurate simply supported boundary conditions for laboratory vibroacoustic tests. Acta Acust. United Acust. 102(1), 170–182 (2016)
Robin, O., Moreau, S., Padois, T., Berry, A.: Measurement of the wavenumber-frequency spectrum of wall pressure fluctuations: spiral-shaped rotative arrays with pinhole-mounted quarter inch microphones. In: Proceedings of the 19th AIAA/CEAS Aeroacoustics Conference, Aeroacoustics Conferences, pp. 1–18 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Robin, O., Franco, F., Ciappi, E., De Rosa, S., Berry, A. (2019). Exact Geometric Similitude Laws for Flat Plate Vibrations Induced by a Turbulent Boundary Layer. In: Ciappi, E., et al. Flinovia—Flow Induced Noise and Vibration Issues and Aspects-II. FLINOVIA 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-76780-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-76780-2_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76779-6
Online ISBN: 978-3-319-76780-2
eBook Packages: EngineeringEngineering (R0)