Doctoral thesis defence of Jacques Cuenca
Tuesday 20th October 2009 at 2 P.M. Salle de conf´erences, LAUM, Universit´e du Maine, Le Mans For obtaining the degree of Doctor of Philosophy
Wave models for the flexural vibrations of thin plates Model of the vibrations of polygonal plates by the image source method Vibration damping using the acoustic black hole effect
Submitted to the examining committee: B.R. Mace W. Desmet J.R.F Arruda E. Foltˆ ete V.V. Krylov V. Martin C. Pezerat F. Gautier L. Simon
Professor, ISVR (Southampton) Professor, Dept. of Mechanical Engineering, K.U. (Leuven) Professor, Faculdade de Engenharia Mecˆ anica, Unicamp (Campinas) Professor, FEMTO-ST (Besan¸con) Professor, Dept. of Aeronautical and Automotive Engg. (Loughborough) CNRS Research Director, IJLRDA (Paris) Professor, LAUM (Le Mans) Professor, LAUM (Le Mans) Professor, LAUM (Le Mans)
Reviewer Reviewer Examiner Examiner Examiner Examiner Examiner Supervisor Co-supervisor
Abstract: Flexural vibrations of thin structures are strongly related to sound radiation and structural damage, for which they deserve careful attention in many domains of science and engineering. Two aspects of crucial importance are the development of accurate tools for the prediction and analysis of vibrations and efficient vibration damping. In the first part of the thesis, a model of the flexural vibrations of thin convex polygonal plates based on the image source method is presented. Considering a polygonal plate excited by a harmonic point source, the image source method consists in describing the successive wave reflections on the boundaries of the plate as contributions from virtual sources obtained by successive symmetries of the original source with respect to the boundaries. The developed approach allows to predict the vibrations of individual plates and plate assemblies of arbitrary convex polygonal geometry and having arbitrary boundary conditions. The method is particularly suitable for mid- and high-frequency dynamics, in that its accuracy is improved with an increase in frequency or structural damping. A tool for estimating the Young’s modulus and structural damping ratio of highly damped flat panels is also proposed. The second part of the thesis concerns vibration damping using the acoustic black hole effect. It is weel-known that a flexural wave travelling in a thin plate or beam slows down in a zone of decreasing thickness. Thus, if the thickness decreases sufficiently smoothly to zero, the wave stops travelling, without being reflected back. Such is the principle of the so-called acoustic black hole effect. A model of the flexural vibrations of such profile is proposed, allowing to determine optimal geometrical and material properties in order to maximise vibration damping. Simulated and measured responses show a reduction of vibration level up to 20 decibels. An alternative implementation of the acoustic black hole effect is investigated, consisting in decreasing wave velocity near the edge of a beam by decreasing its Young’s modulus, by using a shape-memory polymer subjected to a thermal load, which leads to similar vibration reduction levels. Finally, combining the thermoelastic and geometrical approaches leads to significant vibration damping.
