具複合填充物二維聲子晶體之局部共振分析研究

Abstract

本文以有限差分法對聲子晶體進行波傳模擬，並設計特殊聲子晶體以期阻擋低頻頻率。一般以二種材料所組成之聲子晶體對於阻隔低頻之可聽頻率聲波需要大尺寸之幾何結構，本文則利用三種不同材料所構成之聲子晶體進行研究，以嘗試找出較小尺寸之組合。首先，我們以特定之材料組合與合理之尺寸，利用頻散關係圖觀察到的確存在位於低頻的頻溝；但是經由穿射率的探討，此利用三種不同材料之二維聲子晶體阻隔聲波之有效機制主要為共振所造成，且其共振亦發生於低頻時，結果顯示此設計得以大幅縮減週期結構所需之材料及幾何尺寸。然而，並非所有之此類聲子晶體之局部共振模態皆會造成穿射率能量之損失，因此，更藉由分析單一波數下各共振頻率時之單位晶格振動形式，以單位晶格中之位移向量總和較大者能使得低頻彈性波衰減。文中進一步改變週期性低頻聲子晶體排列數目、內部幾何結構進行分析。計算的結果顯示，透過適當的設計與安排可控制共振型聲子晶體之共振頻率與穿射率。

In this thesis, the sonic band gap properties of a two-dimensional periodic three-component composite are investigated. The three-component phononic crystal consists of rubber-coated lead cylinders embedded in an epoxy matrix. The FDTD method was employed to calculate the dispersion and transmission to identify acoustic gaps of three-component phononic crystals. Conventional two-component phononic crystals are not suitable to be applied to block audible and low frequency acoustic waves because of their bulkiness and high cost in applications. However, analysis of the three-component phononic crystal shows a different property to overcome the limitation. From the transmittance spectra and the dispersion relation of the in-plane mode, we see that drop in transmission coefficient corresponding to the frequency in the dispersion curve where group velocity is equal to zero. As a result, there are gaps due to resonant mechanisms in the sonic crystals. Nevertheless, not all local resonances in such phononic crystal can cause decay in the energy transmission coefficient. Therefore, by analyzing the vibrational mode of single wavenumber in unit cell under different resonant frequency, we find that unit cell with greater sum of displacement vector can cause a decay in low frequency elastic wave. Further analysis show that by varying the number of layers, geometric size, and arrangement of the phononic crystals, which consists of lead core and silicone rubber, we can control the resonance frequency and transmission coefficient of resonance type phononic crystal.