Sound Directivity Control in a 3-D Space by a Compact Spherical Loudspeaker Array Alexander Mattioli Pasqual To cite this version: Alexander Mattioli Pasqual. Sound Directivity Control in a 3-D Space by a Compact Spherical Loudspeaker Array. Mechanics [physics.med-ph]. Universidade Estadual de Campinas, 2010. English. ￿NNT: ￿. ￿tel-00530855￿ HAL Id: tel-00530855 https://theses.hal.science/tel-00530855 Submitted on 30 Oct 2010 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. STATE UNIVERSITY OF CAMPINAS FACULTY OF MECHANICAL ENGINEERING PhD PROGRAM IN MECHANICAL ENGINEERING Sound Directivity Control in a 3-D Space by a Compact Spherical Loudspeaker Array Author: AlexanderMattioliPasqual Advisor: ProfessorJoséRoberto deFrança Arruda Co-advisor: Professor PhilippeHerzog 24/2010 STATE UNIVERSITY OF CAMPINAS FACULTY OF MECHANICAL ENGINEERING PhD PROGRAM IN MECHANICAL ENGINEERING DEPARTMENT OF COMPUTATIONAL MECHANICS Sound Directivity Control in a 3-D Space by a Compact Spherical Loudspeaker Array Author: AlexanderMattioliPasqual Advisor: ProfessorJoséRoberto deFrança Arruda(Unicamp,Campinas/Brazil) Co-advisor: ProfessorPhilippeHerzog (LMA, UPR7051,Marseille/France) Program: Mechanical Engineering AreaofConcentration: SolidMechanics and MechanicalDesign A dissertation submitted to the Faculty of Mechanical Engineering in partial fulfillment of therequirementsforthedegreeofDoctorofPhilosophyinMechanical Engineering. Campinas, 2010 S.P. — Brazil i STATE UNIVERSITY OF CAMPINAS FACULTY OF MECHANICAL ENGINEERING PhD PROGRAM IN MECHANICAL ENGINEERING DEPARTMENT OF COMPUTATIONAL MECHANICS PhD DISSERTATION Sound Directivity Control in a 3-D Space by a Compact Spherical Loudspeaker Array Author: AlexanderMattioliPasqual Advisor: ProfessorJoséRoberto deFrança Arruda Co-advisor: ProfessorPhilippeHerzog Committeein charge: ProfessorJoséRoberto deFrança Arruda, Chair Unicamp—Faculty ofMechanical Engineering ProfessorJoséMariaCamposdos Santos Unicamp—Faculty ofMechanical Engineering ProfessorRafael SantosMendes Unicamp—School ofElectricaland ComputerEngineering ProfessorSylvioReynaldoBistafa USP— PolytechnicSchool ProfessorAdolfoMaiaJr. Unicamp—Mathematics,Statisticsand ScientificComputingInstitute Campinas,february 22,2010 ii Acknowledgments First of all, I would like to express my deep gratitude to my advisor José Roberto de França Arruda for his very positiveinfluence and confidence in my work. Thediscussionsand opportuni- tiesheprovidedmehaveproveninvaluabletomypersonal andscientificdevelopment. Iam very grateful to my co-advisorPhilippeHerzog forhis enthusiastictechnical assistance and kind support during my stays at the Laboratory of Mechanics and Acoustics (LMA, CNRS, UPR7051,Marseille,France). SpecialthankstomembersoftheSACADSteamfromtheLMAandtoallstaffatDepartment of Computational Mechanics (DMC, Unicamp, Campinas, Brazil). I am particularly in debt to CédricPinhèdefromLMA—theexperimentalworkcouldnotbedonewithouthisinvaluablehelp anddedication. Also,IwouldliketothanktheundergraduateandgraduatestudentsSamuelPinson, VictorBécard andLucasCóserfortheircontributiontothisworkwithcomplementarysimulations andexperiments. ThankstopeoplefromInterdisciplinaryNucleusforSoundStudies(NICS,Unicamp,Camp- inas, Brazil) for the interesting discussions concerning the musical and practical implementation aspects of directivity controlled sound sources, especially Jônatas Manzolli, Adolfo Maia Jr., Tuti Fornariand JoséAugustoMannis. ForhavingkindlybuiltthemechanicalframeoftheUnicampdodecahedralloudspeakerpro- totype, I thank Jorge Vicente Lopes da Silva, Marcelo Oliveira and their colleagues of the 3-D Technology Division from the Renato Archer Information Technology Center (CTI, Campinas, Brazil). Iamgrateful toFranzZotter(InstituteofElectronicMusicandAcoustics,Graz, Austria)for thetechnicaldiscussionsonsphericalacousticsandtipsthathelpedmetoimprovethismanuscript. I would like to acknowledge the grant sponsored by Coordenação de Aperfeiçoamento de PessoaldeNível Superior (CAPES, Brazil)and thefinancial supportofNationalCenterforScien- iii tificResearch (CNRS, France). I am in debt to my funny uncle Carlos Henrique Mattioli and his son Enzo for their great hospitalityandsupport. SpecialthankstomycousinVivianG.Mattioliwhoallowedmetooccupy herroomduringherabsenceand trustedmetotakecare ofherfrogs. Last butnot least, I wouldliketo warmlythank my parents, brother, sister, grandparents and friends who have encouraged me along this amazing journey in one way or another: Lucas Lima, Flávio Bianchini, Igor Chalfoun, Katlen Allganer, Lúcia Cambraia, Alberto Caeiro, Constance Meiners,CamilaBoscariol,KarenPaulino,RiccardoMariani,FabianoBianchini,LilianaLeonardi, Bruno Costa,Fernanda Calegari,Samer Hamandi,KailingZhu... thankyouall! iv “The greatestchallengetoanythinkeris statingthe problemina way thatwill allowa solution.” Bertrand Russel v Abstract PASQUAL,AlexanderMattioli,SoundDirectivityControlina3-DSpacebyaCompactSpherical LoudspeakerArray. 2010. 171p. Thesis(PhDinMechanicalEngineering): FacultyofMechanical Engineering,StateUniversityofCampinas,Campinas. Angularcontrolofthesoundradiationcanbeachievedbyusingacompactarray ofindepen- dentlyprogrammableloudspeakers operating at thesame frequency range. Thedriversare usually distributedoverasphere-likeframeaccordingtoaPlatonicsolidgeometrytoobtainahighlysym- metrical configuration. Prototypes of compact spherical loudspeaker arrays have been recently developed and applied in room acoustics measurements, electroacoustic music performance and synthesisofdirectivitypatternsofacousticalsources suchas musicalinstruments. However,many aspects concerning their control, design, electromechanical behavior and ability to providea more realisticsoundexperiencethanconventionalaudio systemsremainunclear. This work concerns the analysis and synthesis of sound fields by a compact spherical loud- speakerarrayandaimstocontributetoclarifyingsomeaspectsmentionedabove. Acontrolstrategy basedontheacousticradiationmodesofthesphericalarrayisproposed,whichpresentsseveralad- vantages overthe usual strategy based on the spherical harmonics. A theoretical and experimental analysis of the electromechanical behavior of compact loudspeaker arrays is also presented, in which the acoustic coupling between drivers inside the array frame is taken into account. In addi- tion,optimumdriversignalscorrespondingtoagiventargetdirectivitypatternarederivedusingtwo different cost functions, indicating that the realism of the synthesized pattern may be significantly increased by neglecting the phase of the target directivity pattern. Finally, the proposed theoret- ical models are validated through measurements of electrical impedance, loudspeaker diaphragm velocityand directivitypatterns. vi List of Figures 1.1 Principal radiationdirectionsforaviolinin thehorizontalplane[1]. . . . . . . . . 3 1.2 Synthesisofthetemporalandspatialsignatureofanacousticalsourcebyacompact loudspeakerarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Spherical loudspeakerarray prototypesbasedon thePlatonicsolids. . . . . . . . . 7 2.1 Spherical coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Acousticdipolearbitrarilyorientedmodeledbytwomonopoleswithsource-strengths +Q and Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 s s − 2.3 Longitudinal(on theleft)andlateral (ontheright)quadrupolesarbitrarilyoriented modeledby twodipoleswithmomentsd and d . . . . . . . . . . . . . . . . . 18 m m − 2.4 Directivity patterns of a monopole, a dipole and a lateral quadrupole. The figure shape indicates the magnitude of a normalized sound pressure, and the dark and lightportionsindicatea1800 phasedifference. . . . . . . . . . . . . . . . . . . . . 20 2.5 Directivity patterns of a longitudinal quadrupole evaluated at kr = 0.2, kr = 2, kr = 20 and under farfield condition. The figure shape indicates the magnitudeof anormalizedsoundpressureand thecolorgradient indicatesitsphase. . . . . . . . 20 2.6 Complex-valuedspherical harmonicsupto ordern = 3. . . . . . . . . . . . . . . . 25 2.7 Real-valued sphericalharmonicsup toordern = 3. . . . . . . . . . . . . . . . . . 27 2.8 An acoustic domain (“listening area”), V, bounded by Γ and Γ , free of sound o i sources and scatterers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 vii 2.9 Boundary value problems: a) Interior problem: sound sources and scatterers out- sidethelisteningarea; b)Exteriorproblem: free-field soundradiation. . . . . . . . 35 2.10 Synthesisorplaybackofanacousticfield: a)Irradiationreproduction: Ambisonics and WaveFieldSynthesis;b)Radiationreproduction: compactloudspeakerarray. . 35 3.1 Radiation efficiencies of the first 49 acoustic radiation modes of the continuous sphere(spherical harmonics). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2 Spherical cap withapertureangleθ mountedona rigidsphereatr . . . . . . . . . 41 0 c 3.3 Convexregularpolyhedra(Platonicsolids)and theirmidspheres. . . . . . . . . . . 45 3.4 Radiation efficiency of the ARM # 1 of the continuous sphere and the discrete spheres based on the Platonic solids (linear scale on the left; logarithmic scale on theright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.5 Radiation efficiencyoftheARM #2 to 4ofthecontinuoussphereand thediscrete spheres based on the Platonic solids (linear scale on the left; logarithmic scale on theright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.6 RadiationefficiencyoftheARM#5to9ofthecontinuoussphere,thedodecahedron- like sphere and the icosahedron-like sphere, as well as the ARM # 5 to 6 of the hexahedron-likesphereandtheARM#5to7oftheoctahedron-likesphere(linear scaleon theleft; logarithmicscaleontheright). . . . . . . . . . . . . . . . . . . . 47 3.7 RadiationefficiencyoftheARM#10to16ofthecontinuoussphere,theARM#8 oftheoctahedron-likesphere,theARM#10to12ofthedodecahedron-likesphere and the ARM # 10 to 16 of the icosahedron-like sphere (linear scale on the left; logarithmicscaleon theright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.8 Radiation efficiency of the ARM # 17 to 25 of the continuous sphere and the ARM#17to20oftheicosahedron-likesphere(linearscaleontheleft;logarithmic scaleon theright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.9 SoundpressurepatternscorrespondingtotheARM#1ofthediscretespheresbased on the five Platonic solids. Patterns obtained for ka = 0.1 at a distance r = 10a from thespherecenter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 viii