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String's Double Polarisation and Piano Source Identification

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String's Double Polarisation and Piano Source Identification Piano acoustics : string’s double polarisation and piano source identification Jin Jack Tan To cite this version: Jin Jack Tan. Piano acoustics : string’s double polarisation and piano source identification. Acoustics [physics.class-ph]. Université Paris Saclay (COmUE), 2017. English. NNT : 2017SACLY014. tel- 01755039 HAL Id: tel-01755039 https://pastel.archives-ouvertes.fr/tel-01755039 Submitted on 30 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. NNT : 2017SACLY014 THÈSE DE DOCTORAT DE L’UNIVERSITÉ PARIS-SACLAY PRÉPARÉE ENSTA PARISTECH Ecole doctorale n◦579 L’école Doctorale Sciences Méchaniques et Énergétiques, Matériaux et Géosciences (SMEMaG) Spécialité de doctorat: Acoustique par M. JIN JACK TAN Piano acoustics: string’s double polarisation and piano source identification Thèse presentée et soutenue à Palaiseau le 30 Novembre 2017. Composition du Jury : M. FRANÇOIS GAUTIER Université du Maine (Rapporteur) M. XAVIER BOUTILLON CNRS (Rapporteur) M. BERTRAND DAVID Télécom ParisTech (Président) Mme. JULIETTE CHABASSIER INRIA (Examinatrice) M. KEREM EGE INSA de Lyon (Examinateur) M. CYRIL TOUZÉ ENSTA ParisTech (Directeur de thèse) M. BENJAMIN COTTÉ ENSTA ParisTech (Co-directeur de thèse) To my late uncle, Tan Cheng Kee, and my late aunt, Ch’ng Chin Nigh, both of whom have passed away during the final few months of my thesis preparation. Titre : Acoustique du piano : double polarisation de la corde et identification de sources Mots clefs : modele physique de piano, simulation numerique, corde, chevalet, identification de sources Résumé : L’objectif de cette thèse est d’améliorer la compréhension de l’acoustique du piano dans le contexte de la synthèse sonore par modèles physiques. Le manuscrit est décomposé en trois parties principales, dont les deux premières ont pour but la compréhension de l’origine de la double polarisation de la corde de piano, tandis que la dernière se focalise sur l’identification de sources d’un piano complet. Dans la première partie, la non linéarité géométrique, intervenant lorsque les amplitudes de vibration sont grandes, est étudiée afin de comprendre si le couplage non linéaire peut transmettre de l’énergie à une polarisa- tion non initialement excitée et mener ainsi au phénomène de double polarisation. Un développement en échelles multiples est mené sur un modèle de corde de Kirchhoff-Carrier avec les deux extrémités fixes, restreint au mode fondamental de chacune des polarisations. Les deux oscillateurs ont alors des fréquences très proches, on parle de résonance 1:1. La condition d’existence et le critère de stabilité pour l’apparition de double polarisation sont obtenus et validés numériquement sur la base des équations de Kirchhoff-Carrier, ainsi qu’avec un modèle de corde enrichi. Des expériences sont menées sur un dispositif monocorde où les angles de polarisation naturelle de la corde, le désaccord entre les deux polarisations et le comportement non linéaire son observés et identifiés. La seconde partie se concentre sur le couplage entre la corde et le chevalet. Les degrés de liberté de la corde sont couplés au chevalet dont les mouvements (translation/rotation) sont représentés par un ensemble d’oscillateurs. Les fréquences propres des différents systèmes couplés sont analysés. Des schémas numériques sont proposés et mis en œuvre pour une résolution directe. Ces schémas résolvent les équations de corde par une méthode d’éléments finis d’ordre élevé et les équations du chevalet analytiquement. Les conditions de cou- plage entre corde et chevalet sont assurées par des multiplicateurs de Lagrange. Expérimentalement, la corde est tendue sur le chevalet dans une configuration de type zig-zag et excitée verticalement ou horizontalement. Dans les deux cas, les phénomènes de double polarisation et de double décroissance sont observés et des résultats qualitativement similaires sont obtenus avec les modèles numériques. La dernière partie s’attache à décrire quantitativement les différentes sources vibro-acoustiques d’un pi- ano complet. Une étude est menée en utilisant une analyse des chemins de transfert (transfer path analysis en anglais) sur un piano Bösendorfer 280VC-9. Les contributions de la table d’harmonie, des parties interne et externe de la ceinture, du cadre en fonte et du couvercle sont étudiées dans le domaine fréquentiel. L’analyse montre que la table d’harmonie est le principal contributeur mais que le cadre en fonte et le couvercle jouent également un rôle significatif, en particulier à hautes fréquences. Title : Piano acoustics: string’s double polarisation and piano source identification Keywords : physical modelling of piano, numerical simulation, string, bridge, source identification Abstract : The objective of this thesis is to improve the understanding of the acoustics of the piano in the context of physically-based sound synthesis. The manuscript is decomposed in three parts, the first two being devoted to the understanding of the origin of the double polarisation in piano string, while the third one is dedicated to the identification of sound sources of a complete piano. In the first part, the geometric (large-amplitude) nonlinearity is studied in order to understand if the nonlin- ear coupling can transfer energy to an initially non excited polarisation, thus leading to the double polarisation phenomenon. A multiple-scale analysis is conducted on a Kirchhoff-Carrier string model with fixed boundary conditions at both ends. Each polarisation is restrained to its fundamental mode and thus presenting a 1:1 in- ternal resonance. The existence condition and stability criteria for double polarisation to occur are obtained and validated numerically based on the Kirchhoff-Carrier equations, as well as a more enriched geometrically exact string model. Experiments are carried out on a monochord setup where the natural polarisation angles of the string, detuning between the two polarisations and its nonlinear behaviour are observed and identified. The second part is devoted to the string/bridge coupling. The degrees of freedom of the string are coupled to the bridge whose translational and rotational motions are represented by a set of oscillators. The eigenfrequencies of various coupled systems are analysed. Numerical schemes are proposed and implemented where the string is solved via high-order finite-element method while the lumped bridge is solved analytically and coupled to the string by Lagrange multipliers. Experimentally, the string is strung over a bridge in a zig-zag configuration and excited vertically and horizontally. In both cases, double polarisation and double decay are observed and similar results are also obtained qualitatively in numerical models. The last part is devoted to a quantitative description of the vibroacoustic sources of a Bösendorfer 280VC-9 piano via operational transfer path analysis. The contribution of the soundboard, inner and outer rim, iron frame and lid are investigated in the frequency domain. It is found out that the soundboard is the primary contributor but the iron frame and the lid also play a significant role, especially at high frequencies. Université Paris-Saclay Espace Technologique / Immeuble Discovery Route de l’Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France Acknowledgment This whole thesis would not have been possible without the generous sup- ports from the BATWOMAN Initial Training Network (ITN) (European Commission grant 605867). The BATWOMAN ITN is a Marie Skłodowska- Curie Actions project under the Framework Programme 7 (FP7) fund. I ex- press my utmost gratitude and appreciation for their supports. – see batwoman.eu for more information. I still remembered the night when I first received the email from Antoine Chaigne in March 2014 about my recruitment as a PhD candidate for the so-called "piano project". I was on my way to meet my girlfriend and she was the first person I broke the good news to. Upon reflection, perhaps she foresaw the difficulties of being apart for 3 years back then and broke down in tears. As of writing, I am one day away from fulfilling my contract with my thesis ready to submit and we are still together. These 3 years are simply monumental to me, for which I make a giant step for my career as well as in building my own family. All her dedications, commitment and sacrifices are deeply remembered and I am forever in her debt. Thank you, Sin Yong, for being the pillar despite being more than 10,000km away. Over these three years, I have been very lucky to be under the wings of Cyril Touzé, Benjamin Cotté, Patrick Joly and Antoine Chaigne. They are all incredible supervi- sors and have guided this lost deer to the right track numerously. It has been a wild ride with the final result obtained just weeks before the deadline (thanks Benjamin for showing me the important figure). If anyone thinks of being a student under them or wanting to collaborate on research, I would wholeheartedly recommend them without any hesitation. I have been glad to be part of an amazing Tan family who have been visiting me as often as they could and provide emotional supports whenever I need it despite the time difference and distance. I am sure they are also proud of my achievement. A special shout out to my sister in Manchester whom I visited and freeloaded every year during the Christmas break. In ENSTA, I am blessed to meet some great friends and colleagues. Honorable men- tion to the real Batwoman Àngels Aragonès who understands life as a foreigner in France. I am also fortunate to have met Tommy, Aurélien, Simon and Luca during different time of my stay in ENSTA.
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