結合聲子晶體反射結構之拉福波共振器研製

Design and Fabrication of a Love Wave Resonator Using Phononic Crystals

劉純劭(Chun-Shao Liu)

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(2012年)

https://doi.org/10.6342/NTU.2012.02051

摘要

聲子晶體是一種由週期性彈性材料排列所組成之結構，當彈性波在此結構中傳遞時，因布拉格散射或局部共振而使波傳模態出現不連續的現象，造成彈性波在某些頻率範圍內會被阻擋而無法通過，一般稱此現象為頻溝現象(acoustic band gap)。本文即以數值方法分析結合聲子晶體層狀結構之頻溝現象，包括在波導層表面填充一維及二維週期性洞狀陣列以及具週期性柱狀結構之表面來探討拉福波之頻溝以及局部共振現象。模擬結果顯示可成功求出拉福波通過聲子晶體之頻溝範圍，並據以設計聲波元件。
文中並配合數值模擬分析及微機電製程，探討以聲子晶體為反射體之拉福波共振器行為。以布拉格(Bloch)理論為基礎，使用有限元素法（finite element method, FEM）分析聲子晶體之頻散關係。藉由計算延遲距離（delay distance）定義出等效反射面之位置，搭配穿射係數(transmission coefficient)計算及頻率響應(frequency response)模擬，進而最佳化拉福波共振器之共振效果。
在實驗方面，本研究利用線性調頻交指叉電極(chirped IDT)激發一寬頻訊號以驗證拉福波之頻溝存在性。實驗與數值模擬結果顯示兩者具有一定的程度的吻合性，穿射率在約158MHz到197MHz時有明顯的阻擋效果。

關鍵字

聲子晶體 ； 頻溝 ； 拉福波共振器 ； 有限元素法 ； 品質因數

並列摘要

Phononic crystals (PC) are periodic structures made of different elastic materials. One of the most important phenomena of PC is that the acoustic waves in a specific frequency range cannot propagate through the PC structure due to the band gap. In this thesis, we demonstrate the existence of band gaps and local resonance of Love waves in a piezoelectric substrate coated with a phononic guiding layer which consists of a thin layer and periodic square holes or stubbed pillars. The Love wave band gaps have the potential to be applied to acoustic filters or sensors. In addition, the dispersion relations of phononic layer were calculated by using the finite element method (FEM). To optimize the resonance inside the cavity, the effective reflective plane and transmission coefficient were obtained through a series of numerical simulations.
The MEMS experimental results showed the band gap width and frequency range of a 2D phononic layer coated on a substrate can be successfully measured by the chirped IDTs and the results showed good agreements with the numerical predictions.

並列關鍵字

Phononic crystal ； Band gap ； Love wave resonator ； Finite element method ； Quality factor

參考文獻

[1] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of Periodic elastic composites,” Phys. Rev. Lett. 71, 2022-2025, 1993.

[2] R. Sainidou, B. Djafari-Rouhani, and J. O. Vasseur, “Surface acoustic waves in finite slabs of three-dimensional phononic crystals,” Phys. Rev. B 77, 094304, 2008.

[3] Y. Tanaka and S. I. Tamura, “Surface acoustic waves in two-dimensional periodic elastic structures,” Phys. Rev. B 58, 7958, 1998.

[4] F. Meseguer, M. Holgado, D. Caballero, N. Benaches, J. Sanchez-Dehesa, C. Lopez, and J. Llinares, “Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal,” Phys. Rev. B 59, 12169, 1999.

[5] T. T. Wu, Z. G. Huang, and S. Lin, “Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy,” Phys. Rev. B 69, 094301, 2004.