Analysis of sound wave equations in spherical coordinates using Galerkin weighted residuals method and spherical harmonic functions

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dc.contributor.authorKarasoy, Taner
dc.contributor.authorYagimli, Mustafa
dc.date.accessioned2024-06-13T20:18:27Z
dc.date.available2024-06-13T20:18:27Z
dc.date.issued2024
dc.departmentİstanbul Gedik Üniversitesi
dc.description.abstractPurpose: In this study, it is aimed to bring an unusual mathematical perspective by using semi-analytical mathematical solution methods, unlike the sound intensity determination formulas available in acoustics, and this scientific approach is supported by numerical data. Theory and Methods: Galerkin Weighted Residues Method (WRM) and Spherical Harmonic Functions, which have been used frequently in sound problems in recent years, are used for the solution of sound wave equations in spherical coordinates, which have not been observed in the literature before, in determining the periodic pressure values of sound.Results: Based on the directivity coefficient and spherical harmonic functions in detecting sound pressure levels in the near field, The Critical Distance Threshold, ??????ini, was defined and combined with data from WRM. It has been observed that the Critical Distance threshold value provides very sensitive results in near field distance calculations. The importance of the number of weight functions of WRM in long distance calculations has especially emerged.Conclusion: The critical distance threshold value has an important place in all mathematical analyzes. In the determination of this value, the effect of spherical harmonic functions and the multiplicity of weight functions are clearly seen.
dc.identifier.doi10.17341/gazimmfd.1171452
dc.identifier.endpage942
dc.identifier.issn1300-1884
dc.identifier.issn1304-4915
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85179760337
dc.identifier.scopusqualityQ2
dc.identifier.startpage933
dc.identifier.urihttps://doi.org/10.17341/gazimmfd.1171452
dc.identifier.urihttps://hdl.handle.net/11501/1367
dc.identifier.volume39
dc.identifier.wosWOS:001147255200008
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherGazi Univ, Fac Engineering Architecture
dc.relation.ispartofJournal of the Faculty of Engineering and Architecture of Gazi University
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectSpherical Sound Wave Equations
dc.subjectGalerkin Weighted Residual Methods
dc.subjectSpherical Harmonic Functions
dc.subjectSound Pressure Level
dc.subjectField
dc.subjectDecomposition
dc.subjectTransmission
dc.subjectDucts
dc.titleAnalysis of sound wave equations in spherical coordinates using Galerkin weighted residuals method and spherical harmonic functions
dc.typeArticle

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