{"id":5049,"date":"2020-04-16T13:50:59","date_gmt":"2020-04-16T11:50:59","guid":{"rendered":"https:\/\/itemm.fr\/innovation\/?p=5049"},"modified":"2020-09-22T16:32:58","modified_gmt":"2020-09-22T14:32:58","slug":"etude-des-proprietes-mecaniques-et-vibratoires-du-syahi","status":"publish","type":"post","link":"https:\/\/itemm.fr\/itemm\/etude-des-proprietes-mecaniques-et-vibratoires-du-syahi\/","title":{"rendered":"\u00c9tude des propri\u00e9t\u00e9s m\u00e9caniques et vibratoires du Syahi"},"content":{"rendered":"

Le tabla est une percussion indienne compos\u00e9e de deux futs, le bayan et le dayan repr\u00e9sent\u00e9s sur la figure 1 [1,2]. Le petit fut, dayan, est monoxyl\u00e9, fait de bois taill\u00e9 dans la masse\u00a0; le second fut, bayan, est g\u00e9n\u00e9ralement en m\u00e9tal (laiton, cuivre, aluminium ou acier) et rarement en terre cuite ou bois. Les peaux sont accord\u00e9es sur le dayan en \u00e9tant tendues par des blocs d\u00e9plac\u00e9s avec un marteau. Le tabla est jou\u00e9 avec les mains, en utilisant les doigts ou la paume, et diff\u00e9rents types de frappes existent.<\/p>\n

\"\"<\/a>

Figure 1 : Tabla compos\u00e9 de deux futs, le Bayan et le Dayan<\/p><\/div>\n

Sur la membrane sup\u00e9rieure, une seconde peau est appuy\u00e9e en p\u00e9riph\u00e9rie et un patch est coll\u00e9, ce patch, appel\u00e9 syahi est compos\u00e9 de limaille de fer et de pate de farine ou riz, coll\u00e9s ensembles par couches sur une base de mucilages.<\/p>\n

Il est admis que le syahi est utilis\u00e9e pour rendre le dayan harmonique c\u2019est-\u00e0-dire pour que les diff\u00e9rents modes de vibrations de la membrane soient \u00e0 des fr\u00e9quences proportionnelles entre elles, s\u2019approchant alors d\u2019harmoniques. Cet empilement de fr\u00e9quences cr\u00e9\u00e9 une note et un timbre (tel que les timbales d\u2019orchestre). Pour le bayan, il est aussi utilis\u00e9 pour rendre la membrane harmonique mais peut aussi \u00eatre utilis\u00e9 pour baisser les fr\u00e9quences de r\u00e9sonance, par l\u2019effet de masse ajout\u00e9e.<\/p>\n

Sylvain MAUGEAIS, math\u00e9maticien \u00e0 l\u2019universit\u00e9 du Mans est joueur de tabla et \u00e9tudie cet instrument [3]. Le p\u00f4le d\u2019innovation a travaill\u00e9 avec lui pour caract\u00e9riser les propri\u00e9t\u00e9s m\u00e9caniques de ce patch. Pour ce faire, le comportement vibratoire du patch va \u00eatre utilis\u00e9, mesur\u00e9 avec le protocole repr\u00e9sent\u00e9 sur la figure 2.<\/p>\n

\"\"<\/a>

Figure 2 : dispositif exp\u00e9rimental<\/p><\/div>\n

Le marteau va impacter la mati\u00e8re et la mettre en vibrations. Les vibrations sont capt\u00e9es par un acc\u00e9l\u00e9rom\u00e8tre qui va mesurer l\u2019acc\u00e9l\u00e9ration de la mati\u00e8re (le d\u00e9placement est calcul\u00e9 en int\u00e9grant l\u2019acc\u00e9l\u00e9ration). Lorsque la mati\u00e8re vibre \u00e0 certaines fr\u00e9quences, les vibrations ne sont pas al\u00e9atoires et repr\u00e9sentent des motifs bien particuliers, appel\u00e9s modes de vibration, repr\u00e9sent\u00e9s sur la figure 3. Les forme de ces modes et leurs fr\u00e9quences sont intrins\u00e8quement li\u00e9es \u00e0 la g\u00e9om\u00e9trie de la pi\u00e8ce (sa forme, son \u00e9paisseur) et au mat\u00e9riau (sa densit\u00e9, ses rigidit\u00e9s).<\/p>\n

\"\"<\/a>

Figure 3 : Modes de vibration et fr\u00e9quences du Syahi d\u00e9coup\u00e9. Les modes doubles ne sont pas repr\u00e9sent\u00e9s.<\/p><\/div>\n

Connaissant la g\u00e9om\u00e9trie et la densit\u00e9 il est possible de d\u00e9terminer les propri\u00e9t\u00e9s m\u00e9caniques de rigidit\u00e9 dans les diff\u00e9rentes directions (on parle d\u2019anisotropie) \u00e0 partir des modes de vibration [4]. La rigidit\u00e9 est exprim\u00e9e en Pascal (Pa), et vu les valeurs \u00e9lev\u00e9es on peut l\u2019exprimer en Giga Pascal (GPa). La rigidit\u00e9 est proportionnelle \u00e0 une pression, et lie la d\u00e9formation appliqu\u00e9e \u00e0 une mati\u00e8re \u00e0 la contrainte correspondante. G\u00e9n\u00e9ralement, elle est exprim\u00e9e comme le module d\u2019Young d\u2019un mat\u00e9riau. Les mati\u00e8res solides les moins rigides sont les caoutchoucs, et les plus rigides les nanotubes de carbone.<\/p>\n

Les modes vibratoires ont permis d\u2019identifier les rigidit\u00e9s en flexion et en torsion du syahi. Cependant le patch est d\u00e9j\u00e0 coll\u00e9 sur la peau. Grace \u00e0 une \u00e9tude pr\u00e9alable r\u00e9alis\u00e9e au Laboratoire d\u2019acoustique de l\u2019universit\u00e9 du Mans (LAUM), les propri\u00e9t\u00e9s de la membrane ont d\u00e9j\u00e0 \u00e9t\u00e9 \u00e9valu\u00e9es. Il est alors possible de retrouver les propri\u00e9t\u00e9s du patch seul.<\/p>\n

Ainsi, nous avons observ\u00e9 que celui-ci est particuli\u00e8rement peu rigide par rapport \u00e0 sa densit\u00e9 (ce qui est un moyen d\u2019ajouter de la masse sur une peau sans la rigidifier, et ainsi obtenir le comportement harmonique d\u00e9sir\u00e9). On appelle cela la rigidit\u00e9 sp\u00e9cifique. La densit\u00e9 du patch est proche de 3.2, soit plus \u00e9lev\u00e9 que l\u2019aluminium (2.7), mais sa rigidit\u00e9 est de 7 \u00e0 10 fois plus faible (la rigidit\u00e9 du patch est comprise entre 7 et 12 GPa en fonction des directions, celle de l\u2019aluminium est de l\u2019ordre de 70 GPa).<\/p>\n

A titre d\u2019exemple, la rigidit\u00e9 sp\u00e9cifique de l\u2019aluminium est huit fois plus grande celle du patch. Celle du bois de lutherie \u00e9pic\u00e9a est dix fois plus grande que le patch [5]. Les champions pour cela sont les composites en fibre de carbone, pour lesquels la rigidit\u00e9 sp\u00e9cifique peut \u00eatre jusqu\u2019\u00e0 quarante fois plus \u00e9lev\u00e9e.<\/p>\n

 <\/p>\n

[1] Courtney, David.R,\u00a0 Manufacture and Repair of Tabla. Houston: Sur Sangeet Services (2001).<\/em><\/p>\n

[2] Peter Allen Roda, Resounding Objects: Musical Materialities and the Making of Banarasi Tablas (2013)\u00a0 Ph.D. diss., New York University.<\/em><\/p>\n

[3] Maugeais, S. (2014). How to apply a plaster on a drum to make it harmonic The composite membrane of the tabla. 227\u2013232.<\/em><\/p>\n

[4] Viala, R., Placet, V., & Cogan, S. (2018). <\/em>Identification of the anisotropic elastic and damping properties of complex shape composite parts using an inverse method based on finite element model updating and 3D velocity fields measurements (FEMU-3DVF): Application to bio-based composite violin soundboard. Composites Part A: Applied Science and Manufacturing, 106(December), 91\u2013103. https:\/\/doi.org\/10.1016\/j.compositesa.2017.12.018<\/em><\/p>\n

[5] Viala, R., Placet, V., & Cogan, S. (2019). <\/em>Simultaneous non-destructive identification of multiple elastic and damping properties of spruce tonewood to improve grading – in press. <\/em>Journal of Cultural Heritage<\/em>. https:\/\/doi.org\/10.1016\/j.culher.2019.09.004<\/em><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Le tabla est une percussion indienne compos\u00e9e de deux futs, le bayan et le dayan repr\u00e9sent\u00e9s sur la figure 1 [1,2]. Le petit fut, dayan, est monoxyl\u00e9, fait de bois taill\u00e9 dans la masse\u00a0; le second fut, bayan, est g\u00e9n\u00e9ralement en m\u00e9tal (laiton, cuivre, aluminium ou acier) et rarement en terre cuite ou bois. Les…<\/p>\n","protected":false},"author":3004,"featured_media":21233,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[245,2175],"tags":[2229,2230],"class_list":["post-5049","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-innovation","category-recherche-appliquee-materiaux","tag-syahi","tag-vibratoires","category-245","category-2175","description-off"],"acf":[],"yoast_head":"\n\u00c9tude des propri\u00e9t\u00e9s m\u00e9caniques et vibratoires du Syahi | Itemm -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/itemm.fr\/itemm\/etude-des-proprietes-mecaniques-et-vibratoires-du-syahi\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c9tude des propri\u00e9t\u00e9s m\u00e9caniques et vibratoires du Syahi | Itemm -\" \/>\n<meta property=\"og:description\" content=\"Le tabla est une percussion indienne compos\u00e9e de deux futs, le bayan et le dayan repr\u00e9sent\u00e9s sur la figure 1 [1,2]. 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