Analysis and Control of Elastic Waves in Phononic Structures of Poroelastic Inclusions in a Fluid Athina Alevizaki

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Analysis and Control of Elastic Waves in Phononic Structures of Poroelastic Inclusions in a Fluid Athina Alevizaki Analysis and control of elastic waves in phononic structures of poroelastic inclusions in a fluid Athina Alevizaki To cite this version: Athina Alevizaki. Analysis and control of elastic waves in phononic structures of poroelastic in- clusions in a fluid. Acoustics [physics.class-ph]. Normandie Université, 2018. English. NNT: 2018NORMLH24. tel-01960865 HAL Id: tel-01960865 https://tel.archives-ouvertes.fr/tel-01960865 Submitted on 19 Dec 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. THESE Pour obtenir le diplôme de doctorat Acoustique Préparée au sein de l’Université Le Havre Normandie En partenariat international avec l’Université Nationale et Kapodistrienne d’Athènes GRÈCE Analysis and control of elastic waves in phononic structures of poroelastic inclusions in a fluid Présentée et soutenue par Athina ALEVIZAKI Thèse soutenue publiquement le 28/09/2018 devant le jury composé de Directeur de Recherche CNRS, IJLRA, M. Jean-Marc CONOIR Président Sorbonne Université Paris Chargé de Recherche CNRS, HDR, LAUM, UMR CNRS 6613, M. Jean-Philippe GROBY Rapporteur Le Mans Université Professeur des Universités, LOMC, UMR CNRS 6294, M. Bruno MORVAN Directeur de thèse Université Le Havre Normandie M. Olivier PONCELET Chargé de Recherche CNRS, I2M, Université de Bordeaux Examinateur Maître de Conférences, LOMC, UMR CNRS 6294, M. Pascal REMBERT Encadrant Université Le Havre Normandie Maître de Conférences, LOMC, UMR CNRS 6294, Mme Rebecca SAINIDOU Encadrant Université Le Havre Normandie Professeur des Universités, Section of Solid State Physics, M. Nikolaos STEFANOU Directeur de thèse Université Nationale et Kapodistrienne d’Athènes M. Jérôme VASSEUR Professeur des Universités, IEMN Rapporteur Thèse dirigée par Bruno MORVAN, laboratoire LOMC UMR CNRS 6294 et co-dirigée par Nikolaos STEFANOU, Section of Solid State Physics, Université Nationale et Kapodistrienne d’Athènes i What lies ahead us and what lies behind us is nothing compared to what lies within us... ii iii Preface This dissertation was conducted under the collaboration of two universities: the Uni- versity of Le Havre Normandy and the National and Kapodistrian University of Athens, and I was engaged in researching and writing it from September 2015 to July 2018. I would like to thank my supervisors, Professor Nikolaos Stefanou from the National and Kapodistrian University of Athens, Department of Physics, section of Solid State Physics and Professor Bruno Morvan, Maître de conférences Rebecca Sainidou and Maítre de con- férences Pascal Rembert from the university of Le Havre Normandy, Laboratoire Ondes et Milieux Complexes (LOMC) UMR CNRS 6294, for their excellent guidance and support during this process. They have been my mentors throughout all those years, with their pa- tience and understanding they were able to shape my mind into that of a scientist, teaching me how to reason. Special thanks are owed to Dr. Sainidou and Dr. Rembert, not only for being my primary guides but also for their emotional support and friendly treatment. PhD students are often motivated to pursue the PhD by scientific and humanistic curiosity, the desire to contribute to the academic community, service to others, or personal development. For me all these reasons are summed up to the original Greek meaning of the Doctor of Philosophy, which is “love of wisdom”. The long days spent in the lab, battling shoulder to shoulder with my fellow scientists and friends, the joy for the synthesis, the hope for good results and the sadness and tiredness with each failed attempt, are all characteristics of this process. So, here I would like to thank my colleagues who shared this experience with me, PhD students Petros Pantazopoulos and Adamantia Kosma and Dr. Aristi Christofi. The realization of this PhD would not have been possible without the financial support of the SUPERMEN project, through a postgraduate fellowship. This project is co-financed by the European Union through the European Regional Development Fund and by the Conseil Regional de Haute Normandie. A special thanks to Professor Pascal Pareige, deputy director of LOMC for his help and support in all administrative aspects during my PhD thesis. This thesis is dedicated to my family. If I ever lost interest, they kept me motivated. My parents deserve a particular note of thanks: your wise counsel and kind words have, as always, served me well. A.A. iv v Résumé Dans le présent document de thèse, une extension de la méthode de calcul de la dif- fusion multiple stratifiée est développée en y incluant des structures phononiques àbase de diffuseurs sphériques poroélastiques saturés immergés dans un fluide, en combinant la théorie de Biot avec le formalisme de diffusion multiple. La méthode est alors appliquée à une étude théorique, bien au-delà de l’approximation à grandes longueurs d’onde d’un mi- lieu effectif, de la réponse acoustique d’un milieu granulaire à double porosité saturé, formé d’un réseau cristallin compact de sphères poreuses rigides ou molles. On montre que la vari- ation de la taille des pores et/ou celle de la porosité dans une gamme allant du millimètre au micromètre pour le diamètre des sphères altère d’une façon significative les spectres de transmission, réflexion, et d’absorption d’une couche plane d’épaisseur finie de ces matéri- aux. Les spectres présentés sont analysés par référence aux modes acoustiques de sphères poreuses isolées d’une part, puis par rapport aux diagrammes de dispersion des cristaux infinis correspondants. Une interprétation cohérente de la physique sous-jacente estdon- née. Ces résultats mettent en évidence l’occurrence de nouveaux modes, localisés dans la sphère, provenant des ondes longitudinales lentes propres aux milieux poroélastiques. Ces modes induisent quelques caractéristiques remarquables dans le comportement acoustique de ces matériaux à double porosité, comme des bandes d’absorption non-dispersive larges ou étroites en fréquence et/ou des bandes d’arrêt directionnel. Les propriétés acoustiques de ces structures phononiques à l’échelle sub-micrométrique, i.e. en régime hypersonique (GHz), peuvent être évaluées expérimentalement par diffusion Brillouin. Dans ce docu- ment, une approche théorique élasto-optique rigoureuse, basée sur les fonctions de Green, est proposée afin de décrire la diffusion inélastique de la lumière due aux variations spa- tiotemporelles de l’indice de réfraction du matériau induites par des phonons. Dans ce cadre des expressions analytiques de l’intensité d’un faisceau de lumière diffusé par une particule sphérique dans le vide sont dérivées, permettant ainsi d’améliorer la précision et rapidité des calculs précédents. Les grandes lignes de ce développement théorique jettent les bases pour une description rigoureuse de cet effet dans le cas de cristaux phononiques composés de particules sphériques colloïdales. vi vii PerÐlhyh Sth paroύσα διατριβή anaπτύσσετai mia epèktash thc upologisτικής μεθόδου strwmati- κής poλλαπλής skèdashc gia fwnonikèc domèc από poroelasτικά σφαιρικά s¸mata koresmèna me reustό, συνδυάζοntac th jewrÐa tou Biot me teqnikèc poλλαπλής skèdashc. H mèjodoc εφαρμόζετai sth θεωρητική melèth, pèran thc prosèggishc ενεργού mèsou se μεγάλα μήκη κύματoc, thc akousτικής απόκριshc kokkwd¸n ulik¸n me πόρους se διπλή klÐmaka, embapti- smènwn se υγρό kai se katάσtash κόρου, pou apoτελούντai από sklhrèc ή malakèc πυκνά diatetagmènec por¸deic sfaÐrec. DeÐqnetai όti metabolèc tou megèjouc twn πόρων και/ή tou por¸douc se σφαιρικούς κόκκους diastάσεων thc tάξης tou qiliostού ή kai liγόtero tropopoiούν σημαντικά ta φάσματa dièleushc, ανάκλασης kai απορρόfhshc peperasmènwn plakidÐwn aut¸n twn ulik¸n. Ta φάσματa pou upologÐzontai αναλύοntai αναφορικά tόσο me tic katastάσειc tou akousτικού pedÐou stouc por¸deic σφαιρικούς κόκκους, όso kai me sqe- τικά διαγράμματa διασποράς antÐstoiqwn άπεirwn krustάλλων, parousiάζοntac mia συνεπή ermhneÐa twn υπεύθυνων fusik¸n mhqanism¸n. Ta apotelèsmata mac deÐqnoun thn ύπαρξη nèwn katastάσεων, entopismènwn stic sfaÐrec, oi opoÐec ofeÐlontai sta αργά διαμήκη κύματa pou eÐnai Ðdio qarakthrisτικό twn poroelastik¸n mèswn. Stic katastάσεic autèc ofeÐlontai κάποια axioshmeÐwta qarakthrisτικά thc akousτικής συμπεριφοράς twn υπό melèth ulik¸n me πόρους se διπλή klÐmaka, όπως eureÐec ή stenèc z¸nec απορρόφησης και/ή χάσματa dièleushc se sugkekrimènec διευθύνσειc. Oi akoustikèc ιδιόthtec fwnonik¸n (upo)mikrodom¸n, sthn perioχή twn άπω υπερήχων (GHz), μπορούν na διερευνηθούν, en gènei, me πειράματa skèdashc fwtός Brillouin. Sthn παρούσα διατριβή akoλουθούμε mia ausτηρή πλήρως elastο-οπτική θεωρητική antimet¸pish thc anelasτικής skèdashc fwtός λόgw qwro-qronik¸n metabol¸n tou deÐkth διάθλασης tou mèsou exaitÐac twn fwnonÐwn, basismènh se συναρτήσειc Green, kai katαλήγουμε se analutikèc sqèseic gia tic entάσεic twn σκεδαζόμενων desm¸n fwtός από memonwmèna σφαιρικά swmatÐdia sto κενό, belti¸nontac ètsi thn apotelεσματικόthta kai thn akrÐbeia προηγούμενων upologism¸n. To plaÐsio autό apoteleÐ epÐshc th βάση gia mia ausτηρή periγραφή tou fainomènou gia fwnoνικούς
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