Numerical Modeling of Periodic Acoustic Metamaterial Structure with Helmholtz Resonator Using Transfer Matrix Method

Öz

This study numerically analyzes the sound absorption performance of an acoustic metamaterial composed of periodic Helmholtz resonators. The transfer matrix method (TMM) was employed, and a computational framework incorporating viscothermal and radiative losses was developed. Using the MATLAB-based model, the effects of the number of resonator cells and geometric parameters (particularly neck length) on absorption characteristics were examined. The results show that increasing the number of cells yields more pronounced bandgap regions and enables absorption optimization over a wider frequency range. In addition, variations in neck length directly shift resonance frequencies, highlighting its critical role in tuning the system to target bands. Finally, the loss-related scale factors (Rrad and Rvis) were automatically optimized to maximize the first bandgap width. Overall, the proposed model provides an effective and flexible design-phase tool for evaluating the acoustic performance of metamaterial structures without the need for experimental studies.

Anahtar Kelimeler

• Acoustic metamaterials
• Helmholtz resonator
• Sound absorption
• Transfer matrix method

Transfer Matrisi Metodu ile Helmholtz Rezonatörlü Periyodik Akustik Metamalzeme Yapısının Sayısal Modellemesi

Öz

Bu çalışma, periyodik Helmholtz rezonatörlerinden oluşan bir akustik metamalzemenin ses yutma performansını sayısal olarak analiz etmektedir. Modelleme sürecinde transfer matrisi yöntemi (TMM) kullanılmış; visko-termal ve radyasyon kayıplarını içeren kapsamlı bir hesaplama çerçevesi geliştirilmiştir. MATLAB tabanlı model ile rezonatör hücre sayısı ve geometrik parametrelerin (özellikle boyun uzunluğu) yutum karakteristiğine etkisi incelenmiştir. Sonuçlar, hücre sayısının artmasının daha belirgin band-gap bölgeleri oluşturduğunu ve yutumun daha geniş bir frekans aralığında optimize edilebildiğini göstermiştir. Ayrıca boyun uzunluğundaki değişimin rezonans frekanslarını doğrudan etkilediği ve hedef frekanslara uyarlamada kritik olduğu belirlenmiştir. Son aşamada kayıpları temsil eden ölçek faktörleri (Rrad ve Rvis) otomatik optimize edilerek ilk band-gap genişliği maksimize edilmiştir. Bulgular, önerilen modelin deneysel çalışmaya gerek duymadan tasarım aşamasında metamalzeme yapıların akustik performansını değerlendirmek için etkili ve esnek bir araç sunduğunu göstermektedir.

Anahtar Kelimeler

• Akustik metamalzemeler
• Helmholtz rezonatörü
• Ses yutum
• Transfer matrisi yöntemi

Kaynakça

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