Çeşitli fiziksel boyutlardaki ses denklemlerinden farklı çözüm yöntemleriyle ses şiddetinin belirlenmesinin matematiksel analizi
Yükleniyor...
Dosyalar
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İstanbul Gedik Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Ses basınç düzeyinin tespiti, gürültülü ortamlarda çalışan bireyler için önemli bir etmendir. Ses şiddetini ölçmek için periyodik basınç değişikliklerinin belirlenmesi gerektiğinden bu konuda çok sayıda matematiksel analiz ve deneysel araştırma yapılmıştır. Sesin şiddet ölçümlerinde ve sesin mesafelere bağlı dağılım, azalma ve maruziyet analizlerinde klasik logaritmik denklemler kullanılmaktadır. Bu akademik çalışmada sesin periyodik basınç değerlerinin belirlenmesinde daha önce literatürde gözlemlenmemiş olan küresel koordinatlardaki ses dalga denklemlerinin çözümü için Galerkin Ağırlıklı Artıklar Yöntemi (GAAY) ve son yıllarda ses problemlerinden sıklıkla kullanılmaya başlamış olan fakat ses düzeyi hesaplamalarında (desibel) hiç kullanılmamış olan Küresel Harmonik Fonksiyonlar kullanılmıştır. Yakın alanda ses basıncı seviyelerinin tespitinde yönelme katsayısı ve küresel harmonik fonksiyonlara dayanarak Kritik Mesafe Eşiği r_kri tanımlanmış ve GAAY'dan elde edilen verilerle birleştirilmiştir. Bu sayede elde edilen sayısal ses basıncı değerlerinin klasik logaritmik yaklaşımda kullanılan değerlere oldukça yakın olduğu tespit edilmiş ve bu sayısal veriler için yapılan logaritmik tutarlılık analizi sonucunda klasik logaritmik desibel denklemlerinden elde edilen verilerle yüksek oranda uygunluğu büyük oranda belirlenmiştir. Klasik Logaritmik Yaklaşım referans alınarak yapılan hata payı analizi yüzde cinsinden hesaplanmıştır. Bu yüzde değerleri elde edilirken her N değeri için mesafeye bağlı bulunan desibel değerleri ile Klasik Logaritmik Yaklaşım değerleri çıkartılıp o mesafedeki Klasik Logaritmik Yaklaşım değerleriyle oranlanarak yüzde değerleri tespit edilmiştir. Sonuç olarak hem akustik (ses) bilimine hem de iş sağlığı ve güvenliği bilimine farklı yarı analitik matematiksel çözüm yöntemleri kullanılarak alışılanın dışında matematiksel bir bakış açısı getirilmesi hedeflenmiş ve sayısal verilerle bu bilimsel yaklaşım desteklenmiştir.
Detection of sound pressure level is an important factor for individuals working in noisy environments. Since it is necessary to determine periodic pressure changes to measure sound intensity, many mathematical analyzes and experimental studies have been carried out on this subject. Classical logarithmic equations are used in the intensity measurements of the sound and in the distribution, reduction and exposure analyzes of the sound depending on the distance. In this academic study, Galerkin Weighted Residues Method (WRM) has been used for the solution of sound wave equations in spherical coordinates, which has not been observed in the literature before, in determining the periodic pressure values of sound, and Spherical Harmonic Functions, which have been used frequently in sound problems in recent years, but have never been used in sound level calculations (decibels). Based on the directivity coefficient and spherical harmonic functions in detecting sound pressure levels in the near field, the Critical Distance Threshold r_criwas defined and combined with data from WRM. In this way, it was determined that the numerical sound pressure values obtained were very close to the values used in the classical logarithmic approach, and as a result of the logarithmic consistency analysis made for these numerical data, it was determined that a high level of compatibility with the data obtained from the classical logarithmic decibel equations was determined. The margin of error analysis made with reference to the Classical Logarithmic Approach was calculated in percent. While obtaining these percentage values, the decibel values depending on the distance and the Classical Logarithmic Approximation values were subtracted for each N value and the percentage values were determined by dividing them with the Classical Logarithmic Approximation values at that distance. As a result, different semi-analytical mathematical solution to both acoustic (sound) science and occupational health and safety science. It was aimed to bring an unusual mathematical point of view by using methods and this scientific approach was supported by numerical data.
Detection of sound pressure level is an important factor for individuals working in noisy environments. Since it is necessary to determine periodic pressure changes to measure sound intensity, many mathematical analyzes and experimental studies have been carried out on this subject. Classical logarithmic equations are used in the intensity measurements of the sound and in the distribution, reduction and exposure analyzes of the sound depending on the distance. In this academic study, Galerkin Weighted Residues Method (WRM) has been used for the solution of sound wave equations in spherical coordinates, which has not been observed in the literature before, in determining the periodic pressure values of sound, and Spherical Harmonic Functions, which have been used frequently in sound problems in recent years, but have never been used in sound level calculations (decibels). Based on the directivity coefficient and spherical harmonic functions in detecting sound pressure levels in the near field, the Critical Distance Threshold r_criwas defined and combined with data from WRM. In this way, it was determined that the numerical sound pressure values obtained were very close to the values used in the classical logarithmic approach, and as a result of the logarithmic consistency analysis made for these numerical data, it was determined that a high level of compatibility with the data obtained from the classical logarithmic decibel equations was determined. The margin of error analysis made with reference to the Classical Logarithmic Approach was calculated in percent. While obtaining these percentage values, the decibel values depending on the distance and the Classical Logarithmic Approximation values were subtracted for each N value and the percentage values were determined by dividing them with the Classical Logarithmic Approximation values at that distance. As a result, different semi-analytical mathematical solution to both acoustic (sound) science and occupational health and safety science. It was aimed to bring an unusual mathematical point of view by using methods and this scientific approach was supported by numerical data.
Açıklama
Lisansüstü Eğitim Enstitüsü, İş Sağlığı ve Güvenliği Ana Bilim Dalı
Anahtar Kelimeler
Küresel Ses Dalga Denklemleri, Galerkin Ağırlıklı Artıklar Yöntemi, Küresel Harmonik Fonksiyonlar, Ses Basıncı Düzeyi, Spherical Sound Wave Equations, Galerkin Weighted Residual Method, Spherical Harmonic Functions, Sound Pressure Level
