Alain LE BOT  Chargé de Recherche CNRS Laboratoire de tribologie et dynamique des systèmes UMR CNRS 5513 Ecole centrale de Lyon 36, av. Guy de Collongue, 69134 Ecully FRANCE Tel : +33 (0)4-72-18-62-75 E-mail : Alain.Le-Bot@ec-lyon.fr

Position

Graduated in both Engineering degree and Master of Mathematics, Alain Le Bot started his career in Institut National Polytechnique Felix Houphouët Boigny (INPHB previously named INSET) in Yamoussoukro, Ivory Coast as teacher in mathematics during two years. Being back in France, he joigned EDF compagny (Electricity of France) as engineer in the department Acoustique et mécanique vibratoire for four years. Doctor in acoustics in 1994 and Habilité à diriger des recherches in 2002, Alain Le Bot is currently Chargé de recherche CNRS in the Laboratory of tribology and dynamics of systems (LTDS UMR CNRS 5513, Ecole centrale de Lyon, Ecole nationale d'ingénieurs de Saint-Etienne, Ecole nationale supérieure des mines de Saint-Etienne).

Research activity

A. Le Bot's main areas of research concern acoustics, vibration and tribology. Jointly with several co-workers and PHD-students, his activity is conducted in the team Nanotribology, friction and vibroacoustics managed by J. Perret-Liaudet et D. Mazuyer. His topics of research are the followings:

i)Statistical energy analysis (SEA). Statistical Energy Analysis is a theory of energy exchanges in vibroacoustical systems. Proposed in the sixties by Lyon, Sharton, Maidanik, Smith, Ungar... SEA is the analogous of thermodynamics for audio frequencies. Introducing the concept of vibrational temperature, SEA is based on the assumption that the exchanged powed between adjacent vibrational systems is proportional to the difference of vibrational temperatures. Although SEA is commonly applied in engineering, it is still in development. Our work aims to clarify the foundations of SEA and especially the assumption of "diffuse field" which can also be enounciated as the theorem of "equipartition of energy". The study of non-diffuse field in SEA is related to the non-equilibrium theory of thermodynamics.

Fig. 1. Statistical Energy Analysis in vibroacoustics. A complex structure is divided in several sub-systems. These sub-systems can store vibrational energy (tank volume), can receive energy from noise sources (tap), can dissipate energy (evaporation) and finally, can exchange energy with neighbour sub-systems (pipe).

ii)Radiative transfert equation in vibroacoustics. When the energy field is non-diffuse in vibroacoustics, SEA no longer applies. The question then arises of which theory can predict the repartition of energy within sub-systems. We have proposed a theory based on the radiative transfert equation applied to acoustical and structural rays. In this theory, energy balance equations are written at any point within sub-systems and at the interface of sub-systems instead the global energy balance equations of SEA. This theory has been implemented in the software CeReS ans has been successfuly applied to many examples such as assembled plates, coupled rooms, radiating plates, structural response and diffraction.

Fig. 2. Radiative transfert in vibroacoustics. Repartition of sound around a car engine. The sound field is largely non diffuse (Prediction of CeReS software, from thesis of Emeline Sadoulet-Reboul).

iii)Dynamics of multi-contact interfaces. When two solids slide on each other, it is well-known that a friction force opposes to the movement. After several centuries of stagnation, tribology made progress with the discovery of Bowden and Tabor that the relatively rare contact of antagonist asperities can explain Amontons-Coulomb's laws. Although this theory is still in discussion, it is commonly admitted that the multi-contact interface is the key of the understanding of friction. Our work aims to study the dynamics of multi-contact interfaces. Several phenomena are under investigation. We study friction noise and more particularly roughness noise that is the noise which originates from the shocks between antagonist asperities. Wear by vibro-impacts is the second subject. Is is encountered, for instance, in systems where a shaft vibrates into its bearing with a relatively low level but a long duration.

Fig. 3. The actual contact between two solids is achieved by a large number of small spots. Left, asperities in contact between two rough surfaces. Right, view of contact between glass and elastomer, the contact spots are colored in red (full scale ~ 100 micrometers, from thesis of Fabrice Deleau).

iv)Uniski for disabled men. Skiing for disabled men is a relatively recent practice. The beginning was in the eighties and this practice has now gained in popularity. The most famous official competition is the Paralympic games. In this framework, we have designed and manufactured some uniskis intended for the highest level of competition. In the Paralympic games of Lillehammer 1994, Norway, Ludovic Rey-Robert won the gold medal in downhill and slalom events whereas Alain Marguerretaz won the bronze medal in Super-G event with our uniskis. Nowadays, Denis Barbet, gold medal in Paralympic games of Turin 2006, has the benefit of our technical help to prepar his races.

Fig. 4. Uniski for disabled men. Ludovic Rey-Robert and Alain Marguerretaz during the Paralympic games Lillehammer 1994.

Thesis

[1] Thèse de doctorat spécialité acoustique, "Équations énergétiques en mécanique vibratoire, application au domaine des moyennes et hautes fréquences", École centrale de Lyon, France, soutenue le 20 avril 1994.

Publications in journals

[1] A. Le Bot and E. Luzzato, "Étude des problèmes d'identification des sources acoustiques en basses fréquences", EDF bulletin de la DER Série A, vol. 4, pages 9-44, 1990.

[2] A. Le Bot, M.N. Ichchou and L. Jezequel. "Energy flow analysis for curved beams," Journal of the Acoustical Society of America, vol. 102(2), pages 943-954, 1997.

[3] M.N. Ichchou, A. Le Bot and L. Jezequel. "Energy models of one-dimensional, multi-propagative systems," Journal of Sound and Vibration, vol. 201(5), pages 535-554, 1997.

[4] A. Le Bot. "Geometric diffusion of vibrational energy and comparison with the vibrational conductivity approach," Journal of Sound and Vibration, vol. 212(4), pages 637-647, 1998.

[5] A. Le Bot. "A vibroacoustic model for high frequency analysis," Journal of Sound and Vibration, vol. 211(4), pages 537-654, 1998.

[6] A. Le Bot and A. Bocquillet. "Comparison of an integral equation on energy and the ray-tracing technique for room acoustics," Journal of the Acoustical Society of America, vol. 108(4), pages 1732-1740, 2000.

[7] V. Cotoni and A. Le Bot. "Radiation of plane stuctures at high frequency using an energy method," International Journal of Acoustics and Vibration, vol. 6(4), pages 209-214, 2001.

[8] M. N. Ichchou and A. Le Bot and L. Jezequel. "A transient local energy approach as an alternative to transient SEA: wave and telegraph equations," Journal of Sound and Vibration, vol. 246(5), pages 829-840, 2001.

[9] A. Le Bot. "Energy transfer for high frequencies in built-up structures," Journal of Sound and Vibration, vol. 250(2), pages 247-275, 2002.

[10] V. Cotoni and A. Le Bot and L. Jezequel, "High frequency radiation of L-shaped plate by a local energy flow approach," Journal of Sound and Vibration, vol. 250(3), pages 431-444, 2002.

[11] A. Le Bot. "A functional equation for the specular reflection of rays," Journal of the Acoustical Society of America, vol.112(4), pages 1276-1287, 2002.

[12] V. Cotoni and A. Le Bot and L. Jezequel. "Sound transmission through a plate by an energy flow approach," Acustica with Acta Acustica, vol. 88(6), pages 827-836, 2002.

[13] V. Cotoni and A. Le Bot. "Specular and diffuse reflections of rays in coupled thin plates at high frequencies," Journal of Sound and Vibration, vol. 265, pages 23-41, 2003.

[14] E. Reboul and A. Le Bot and J. Perret-Liaudet. "Introduction of the Acoustical diffraction in the radiative transfer method," Comptes Rendus Mécanique, vol. 332(7), pages 505-511, 2004.

[15] A. Le Bot. "Comparison of vibrational conductivity and radiative energy transfer methods," Journal of Sound and Vibration, vol. 283, pages 135-151, 2005.

[16] E. Reboul and A. Le Bot and J. Perret-Liaudet. "Radiative transfer equation for multiple diffraction," Journal of the Acoustical Society of America, vol. 118(3), pages 1326-1334, 2005.

[17] A. Le Bot. "Energy exchange in uncorrelated ray fields of vibro-acoustics," Journal of the Acoustical Society of America, vol. 120(3), pages 1194-1208, 2006.

[18] A. Le Bot. "Derivation of Statistical Energy Analysis from radiative exchanges," Journal of Sound and Vibration, vol. 300, pages 763-779, 2007.

[19] G. Boyer, H. Zahouani, H., A. Le Bot, L. Laquieze. "In vivo characterization of viscoelastic properties of human skin using dynamic micro-indentation," IEEE Engineering in Medicine and Biology Society, vol. 26, pages 4584-4587, 2007.

[20] E. Sadoulet-Reboul, A. Le Bot, J. Perret-Liaudet and M. Mori, H. Houjoh. "A hybrid method for vibroacoustics based on the radiative energy transfer method," Journal of Sound and Vibration, vol. 303(3), pages 675-690, 2007.

[21] G. Boyer, L. Laquieze, A. Le Bot, S. Laquieze and H. Zahouani. "Dynamic indentation on human skin in vivo: ageing effects," Skin Research and Technology, vol. 14, pages 1-13, 2008.

[22] E. Sadoulet-Reboul, A. Le Bot and J. Perret-Liaudet. "A hybrid method for vibroacoustic coupling, Application to the noise radiated around an engine compartment," Revue Européenne de Mécanique Numérique, European Journal of Computational Mechanics, vol. 17, pages 689-699, 2008.

[23] H. Ben Abdelounis, K. Elleuch, R. Vargiolu, H. Zahouani, A. Le Bot. "On the behaviour of obsidian under scratch test," Wear, vol. 266, pages 621-626, 2009.

[24] A. Le Bot. "Entropy in Statistical Energy Analysis," Journal of Acoustical Society of America, vol. 125, pages 1473-1478, 2009.

[25] H. Ben Abdelounis, A. Le Bot, J. Perret-Liaudet, H. Zahouani. "An experimental study on roughness noise of dry rough flat surfaces," Wear, vol. 268, pages 335-345, 2010.

[26] A. Le Bot and E. Bou Chakra. "Measurement of friction noise versus contact area of rough surfaces weakly loaded," Tribology Letters, vol. 37, pages 273-281, 2010.

[27]A. Le Bot and V. Cotoni. "Diagrams for the validity of Statistical Energy Analysis," Journal of Sound and Vibration, vol. 329, pages 221-235, 2010.

Conferences

[1] E. Luzzato and A. Le Bot. "Numerical determination of sound source radiation using near field intensity in low frequency range," International Congress on Recent Developments in Air and Structure Born Sound and Vibration, Auburn university USA, pages 35-42, 6 - 8 march 1990.

[2] A. Le Bot and L. Jezequel. "Energy formulation for one dimensional problems," Acoutic's 93, Southampton United Kingdom, pages 561-568, march 1993.

[3] A. Le Bot and L. Jezequel. "Energy methods applied to transverse vibrations of beams," 4th International Congress on Intensity, Senlis France, pages 371-378, 31 aug. - 2 sept. 1993.

[4] A. Le Bot, M.N. Ichchou and L. Jezequel. "Smooth energy formulation for multi-dimensional problems," Euro-Noise 95, Lyon France pages 423-428, 21 - 23 march 1995.

[5] A. Adobes and A. Le Bot. "The use of a balance on reactive power to improve SEA theory," Inter-Noise 95, Newport Beach USA, pages 1259-1262, 10 - 12 july 1995.

[6] A. Le Bot and L. Ricol. "Integral equation instead of heat conduction equation for medium and high frequencies," Inter-Noise 95, Newport Beach USA, pages 579-582, 10 - 12 july 1995.

[7] A. Le Bot, M.N. Ichchou and L. Jezequel. "Formulation énergétique pour l'étude moyennes et hautes fréquences des structures," Premier Colloque du Groupement de Recherche Vibroacoustique GDR 1138, Marseille France, pages 1-12, 14 - 15 déc. 1994. Publications du LMA-CNRS, ISBN 2-909669-06-8, 1995.

[8] M.N. Ichchou, A. Le Bot and L. Jezequel. "Couplage de plaques en hautes fréquences : méthode de l'équation de la chaleur," Second Colloque du Groupement de Recherche Vibroacoustique GDR 1138, Marseille France, pages 65-79, 20 - 21 mars 1996. Publications du LMA-CNRS, ISBN 2-909669-07-6, 1996.

[9] A. Le Bot, M.N. Ichchou and L. Jezequel. "Couplage de plaques en hautes fréquences : formulation intégrale et perspectives acoustiques," Second Colloque du Groupement de Recherche Vibroacoustique GDR 1138, Marseille France, pages 81-92, 20 - 21 mars 1996. Publications du LMA-CNRS, ISBN 2-909669-07-6, 1996.

[10] A. Le Bot and L. Jezequel. "Integral formulation for high frequencies in assembled plates," 4th French Congress on Acoustics, Marseille France, 4 pages, 14 - 18 april 1997.

[11] A. Le Bot, "A new method for the non modal domain," Comett'95, Lyon France, pages 465-474, 5 - 6 oct. 1995. Published in New advances in modal synthesis of large structures, Edited by L. Jezequel, A.A. Balkema, Rotterdam, ISBN 90 5410 859 2, 1997.

[12] M.N. Ichchou, P. Moron, A. Le Bot and L. Jezequel. "Synthèse comparative de quatre méthodes prédictives pour le domaine non modal," Troisième Colloque du Groupement de Recherche Vibroacoustique GDR 1138, Le Mans France, pages 177-185, 3 - 4 mars 1997. Publications du LMA-CNRS, ISBN 2-909669-08-4, 1997.

[13] A. Le Bot and A. Bocquillet. "Geometrical acoustics and integral representation of energy fields," Inter-Noise 98, Christchurch New Zealand, 4 pages, 16 - 18 nov. 1998.

[14] A. Le Bot, A. Bocquillet, M.N. Ichchou and L. Jezequel. "Exemples d'application d'une formulation intégrale hautes fréquences," Quatrième Colloque du Groupement de Recherche Vibroacoustique GDR 1138, Le Mans France, pages 85-91, 11 - 13 mars 1998. Publications du LMA-CNRS, ISBN 2-909669-13-0, 1998.

[15] V. Cotoni, A. Le Bot, M.N. Ichchou and L. Jezequel, "Line excited curved panels radiation at high frequency by a power flow method," Novem 2000, Lyon France, 11 pages, 31 aug. - 2 sept. 2000.

[16] A. Bocquillet, M.N. Ichchou, A. Le Bot and L. Jezequel, "SEA and local energy approach of fluid-filled pipes," Novem 2000, Lyon France, 12 pages, 31 aug. - 2 sept. 2000.

[17] M.N. Ichchou, A. Le Bot and L. Jezequel, "Applications of the local energy approach in elastoacoustic engineering," Novem 2000, Lyon France, 12 pages, 31 aug. - 2 sept. 2000.

[18] V. Cotoni, A. Le Bot and L. Jezequel, "High frequency plate radiation by power flow analysis with experimental validation," Inter-Noise 2000, Nice France, 4 pages, 27 - 30 aug. 2000.

[19] A. Le Bot, J. Perret-Liaudet, E. Rigaud and N. Driot, "A hybrid model for the prediction of noise radiated by gearbox," Inter-Noise 2002, Deaborn Michigan USA, 5 pages, 19 - 21 aug. 2002.

[20] A. Le Bot and T. Mathia, "Monoski for disabled men," 6th Conference of the European Association for Research in Adapted Physical Activity, Amien France, 3 pages, 30 oct. - 2 nov. 2002.

[21] A. Le Bot, T. Schmitt, N. Driot and J. Perret-Liaudet, "Radiative transfer equation for time-reverberation of concert halls," 10th International Congress on Acoustics and Vibration, Stockholm, Sweden, 7-10 july 2003.

[22] E. Reboul, A. Le Bot and J. Perret-Liaudet, "Application of the radiosity method to acoustical diffraction in high frequency range," Internoise 2003, Seogwipo, Korea, 25-28 aug. 2003.

[23] N. Driot, A. Le Bot and J. Perret-Liaudet, "Variability of the predicted reverberation time of a concert hall induced by absorption coefficient uncertainties," Internoise 2003, Seogwipo, Korea, 25-28 aug. 2003.

[24] E. Reboul and A. Le Bot and J. Perret-Liaudet. "A hybrid method for the radiated noise prediction in high frequency," 18th International Congress on Acoustics, Kyoto, Japan, 4 - 9 april 2004.

[25] F. Flament and R. Vargiolu and A. Le Bot and A. Mavon and H. Zahouani. "Étude du vieilissement par mesure mécano-acoustique," Colloque de la Société francophone de l'ingénierie cutanée, Liège, Belgique, 8 - 9 september 2004.

[26] E. Reboul and J. Perret-Liaudet and A. Le Bot. "Acoustical energy diffracted around a building ," CFA/DAGA04, Strasbourg, France, 22 - 25 march 2004.

[27] A. Le Bot and H. Abdelounis and H. Zahouani. "Experimental study of friction noise of dry contact under light load," 1th International Congress on Design and Modelling of Mechanical Systems, Hammamet, Tunisia, 23 - 25 march 2005.

[28] A. Le Bot. "Application of radiative transfer to vibroacoustics," 2th International Congress on Noise and Vibration: Emerging Methods NOVEM, St Raphael, France, 18 - 21 april 2005.

[29] E. Reboul and J. Perret-Liaudet and A. Le Bot and M. Masato and H. Houjoh. "Vibroacoustic prediction of mechanisms using a hybrid method," 2th International Congress on Noise and Vibration: Emerging Methods NOVEM, St Raphael, France, 18 - 21 april 2005.

[30] A.L. Kaiser and A. Le Bot and S. Bec and C. Langlade and J.P. Vernot. "Influence des paramètres mécaniques sur l'usure d'un contact tube-bague en conditions extrêmes," 17ième Congrès français de mécanique, Troyes, France, 29 août - 2 september 2005.

[31] E. Reboul and A. Le Bot and J. Perret-Liaudet. "Approche hybride pour la maîtrise vibroacoustique de mécanismes," 17ième Congrès français de mécanique, Troyes, France, 29 août - 2 september 2005.

[32] A. Le Bot "From non diffuse field to Statistical Energy Analysis," Euronoise 2006, Tampere, Finland, 30 may - 1 june 2006.

[33] H. Ben Abdelounis and A. Le Bot and H. Zahouani. "Description phénoménologique du bruit de rugosité," 15ième journées francophones de la tribologie, Lille, France, 22 - 24 may 2006.

[34] A. Le Bot, H. Zahouani, R. Vargiolu and A. Mavon. "Assessment of the smoothness of surfaces with an acoustical probe," 14th International Congress on Acoustics and Vibration, Cairns, Australia, 9-12 july 2007.

[35] G. Boyer, H. Zahouani, A. Le Bot and L. Laquieze. "In vivo characterization of viscoelastic properties of human skin using dynamic micro indentation," 29th Int. Conf. of the IEE Engineering in Medecine and Biology Society, Lyon, France, 4 pages, 23-26 august 2007.

[36] J.M. Georges, I. Antoine, S. Carvallo, J. Cayer-Barrioz, A. Le Bot. "Human friction, Material friction," 4th Int. Conference on enactive interfaces, Grenoble, France, 19-22 november 2007.

[37] H.B. Abdelounis, A. Le Bot, H. Zahouani, J. Perret-Liaudet. "Experimental study on friction noise of dry rough surfaces," Proceedings of the STLE/ASME International Joint Tribology Conference IJTC2008, Miami, Florida, USA, 20-22 october 2008.

[38] E. Bou Chakra, A. Le Bot. "Friction induced-vibration in a rough dynamic contact," 16th International Colloquium Tribology Lubricants, Material and Lubrication engineering, Stuttgart, Germany, 4 pages, 15-17 january 2008.

[39] A. Le Bot, V. Cotoni. "Discussion on the validity domain of Statistical Energy Analysis," Acoustics’08, Paris, France, 4 pages, 29 june - 4 july 2008.

[40] F. Deleau, D. Mazuyer, J. Perret-Liaudet, A. Le Bot, E. Rigaud, A. Koenen. "Dynamic instability visualization of a rubber/glass interface," Internoise’08, Shanghai, China, 10 pages, 26 - 29 october 2008.

[41] H. Ben Abdelounis, H. Zahouani, A. Le Bot, J. Perret-Liaudet. "Numerical and experimental analysis of roughness noise," 12th International Conference on Metrology & Properties of Engineering Surfaces, Rzesz, Poland, 5 pages, 8 - 10 july 2009.

[42] A. Le Bot. "Equilibrium and non-equilibrium in Statistical Energy Analysis," Noise and Vibration : Emerging methods NOVEM 2009, Oxford, United Kingdom, 9 pages, 5 - 8 april 2009.

[43] A. Le Bot. "Statistical Energy Analysis and the second principle of thermodynamics," IUTAM Symposium : The vibration analysis of structures with uncertainties, St Petersbourg, Russia, 11 pages, 6 - 9 July 2009.

[44] J. Perret-Liaudet, Fabrice Deleau, Alain Le Bot, Denis Mazuyer, Alain Koenen. "On some experimental results about nonlinear self-induced vibrations of a rubber/glass interface in relation with squealing," 16th International Congress on Sound and Vibration, Krakow, Poland, 5 - 9 july 2009.

[45] B. Stoimenov, A. Le Bot, K. Adachi, K. Kato, H. Zahouani. "The level of rubbing sound in relation to surface roughness in different systems," World Tribology Congress, Kyoto, Japan, 6 - 11 september 2009.

[46] A. Le Bot, Dynamics of multicontact interfaces," Ecole de Cargese, theoretical modeling and experimental simulation in tribology, Cargese, France, 22 - 26 march 2010.

[47] F. Bavouzet, J. Cayer-Barrioz, A. Le Bot, F. Brochard, A. Buguin. "Adhesive friction law for patterned elastomeric surfaces," Adhesion Society Meeting, Daytona Beach, Florida, USA, 21-24 february 2010.

Patent and softwares

[1] L. Billet and A. Le Bot, "Appareillage permettant la pratique du ski alpin à un skieur handicapé des jambes, et ski équipé", Brevet INPI 95903831.6-2315 1994.

[2] "CeReS", This software is intended to the prediction of vibrational levels and sound pressure levels in the high frequency range. Based on the geometrical acoustics/optics and its extension, the geometrical theory of diffraction, CeReS solves the radiative transfer equation. It applies in various fields such as structural dynamics, acoustics, optics and seismology. Copyright Alain Le Bot 1997, 2000, 2006

[3] "Free awale", An implementation of the famous African game with an improved min-max algorithm. Free awale is distributed under the GNU GPL licence and can be freely downloaded.

[4] "Group", A small software intented to illustrate the theory of finite groups. Group is distributed under the GNU GPL licence and can be freely downloaded.