聲子晶體平板共振腔內薄膜微陣列之局部共振行為探討

Local Resonances of Membrane Arrays in a Phononic Plate Cavity

廖辰峰(Chen-feng Liao)

指導教授 ： 吳政忠

國立臺灣大學/工學院/應用力學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.00056

摘要

聲子晶體為材料性質以週期性排列的彈性結構，當聲波在聲子晶體結構中某頻段內，沿任何方向均無法傳遞時則稱之為全頻溝(complete band gap)。若將週期性聲子晶體結構移除數排，形成的線缺陷使原頻溝內無任何模態，將使缺陷形成一共振腔結構。
本論文以設計聲子晶體共振腔內薄膜微陣列為目的，搭配有限元素法(finite element method)與布拉格(Bloch theorem)理論作為分析基礎。首先，計算二維矽基薄膜結構之頻散曲線，而在頻散曲線關係中沿著第一布里路因區Γ-Χ中有群速度為零的部分即為局部共振態，並以第一共振模態作為分析的主角。為了設計聲子晶體共振腔，本文將薄膜第一共振態頻率落在聲子晶體頻溝(band gap)範圍內16~18MHz，因此在計算頻散關係後，能將薄膜陣列置於聲子晶體內成為一共振腔結構。本文採用高機電耦合係數的壓電基底材料128oYX-LiNbO3，並在壓電基底上放置電極以激發出雷利波(Rayleigh wave)作為波源。若表面波的傳播路徑上放置耦合層則產生表面波匹配現象，因此表面波能量將傳遞至共振腔結構並產生第一局部共振態。
為了讓薄膜陣列在表面波匹配效應下能有更佳的振幅，本文優化耦合層厚度與有效距離，使共振腔因建設性干涉下薄膜振幅有顯著的增強。最後預期模擬的結果能在未來作為微混合器等應用面上的啟發。

關鍵字

聲子晶體頻散 ； 聲子晶體共振腔 ； 薄膜局部共振模態 ； 雷利波 ； 表面聲波匹配現象

並列摘要

A Phononic crystal (PC) is a kind of structure whose mechanical properties are periodically arranged. The most important character of the phononic crystal is the band gap phenomenon, which means that there is no any wave to propagate in such kind of structure in specific frequency range. If we remove rows of structure in PC, the phononic structure will be a resonator
In this thesis, we compute the local resonances membrane arrays in a phononic plate cavity by using the finite element method. The dispersion relation of the membrane was obtained by simulation then we chose the first local resonant mode as a main structure. In order to design the resonator, we compute the dispersion relation of the two-dimensional air/silicon phononic structure, then the first local resonant frequency of the membrane is in the phononic band gap. After that, we used the Rayleigh wave as an energy source, which was generated by two designs of interdigitated electrodes on 128oYX-LiNbO3 substrate. When the Rayleigh wave travels along the surface of the substrate with coupling agent on its path, the energy of the Rayleigh wave will be coupled into the coupling layer as a Rayleigh leaky wave, as a result the membrane arrays will vibrate on the first local resonant mode.
In order to optimize the amplitude of the membrane arrays, we discussed the impact of the coupling layer thickness and the effect distance to explore the results of resonant cavity formed by constructive interference. Finally, under the constructive interference there has a significant increase in the amplitude of the resonant cavity and the simulation results can be expected as a micromixer in the future.

並列關鍵字

Dispersion relation of phononic crystal ； Phononic plate cavity ； Local resonant mode of membrane ； Rayleigh wave ； Leaky SAW

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