Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi

Bu çalışmada farklı tasarımlardaki fononik kristallerin dispersiyon özellikleri deneysel olarak FFT algoritması ve nümerik olarak sonlu elemanlar yöntemi kullanılarak araştırılmıştır. Periyodik olarak yerleştirilmiş kompozit silindirlerden oluşan kare örgü ve yarı-periyodik (Fibonacci dizilimi) yapıdaki iki boyutlu fononik kristal de, birinci Brillouin bölgesinde dalga vektörüne (k) karşılık frekanslar elde edilerek M–Г–X–M yolu boyunca fononik bant yapıları çizdirildi. Periyodik fononik kristal tasarımlarından dolu kompozit silindirlerden oluşan yapıda 4 kHz–7 kHz aralığında Г–X yönünde kısmi bant, nümerik olarak incelenen c-şekilli fononik kristalde 2 kHz–3 kHz aralığında tam bant, Fibonacci dizilimindeki fononik kristalde ise 3 kHz–4 kHz ve 3,5 kHz–6,7 kHz aralıklarına Г–X yönünde kısmi bantlar gözlendi. Sonuçların geçerliliğini test etmek için sonlu yapıda iletim kayıpları nümerik olarak hesaplandı ve deneysel olarak ölçüldü. Fononik bant yapısı ile elde edilen iletim kayıpları karşılaştırıldığında sonuçların uyumlu oldukları gözlendi.

Dispersion Features of the Sound Waves in Phononic Crystals: Finite Element Analysis

In this study, dispersion properties of phononic crystals in different design were investigated experimentally by using FFT algorithm and numerically by using finite elements method. In the first Brillouin zone, frequencies corresponding to the wave vector (k) obtained and phononic band diagram were plotted along the M–Г–X–M path for the two dimensional phononic crystals which were periodically placed composite cylinders with square lattice and quasi-periodic (Fibonacci sequence). In the periodic phononic crystal designs, partial band in Г–X direction between 4 kHz–7 kHz in the structure consist of full composite cylinders, full band between 2 kHz–3 kHz range in the numerically studied C-shaped phononic crystal, and partial bands in Г–X direction between in the 3 kHz–4 kHz and 3.5 kHz–6.7 kHz ranges in Fibonacci phononic crystal were observed. In order to compare validity of the results, in the finite structure the transmission losses were calculated numerically and measured experimentally. When the phononic band structure compare with the obtained transmission losses, it was observed that the results were compatible.

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