結合聲子晶體反射結構之雙頻板波共振器研製

Fabrication of a Dual Frequency Lamb Wave Resonator Using Phononic Gratings

藍智偉(Chih-Wei Lan)

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(2011年)

https://doi.org/10.6342/NTU.2011.00326

摘要

聲子晶體是由多種彈性材料周期性排列而成。而當彈性波在此結構中傳遞時，波傳模態在某些特殊頻帶會出現不連續的現象，亦即彈性波無法在該頻帶內傳遞，一般稱此現象為頻溝現象(acoustic band gap)。本研究即利用此頻溝現象，配合數值分析及微機電製程，探討以聲子晶體為反射體之共振器及濾波器行為。
本文以布拉格(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。此外，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，進而最佳化雙頻共振器之共振效果。本文也同時包含階梯式濾波器(ladder type filter)之探討，藉由耦合雙頻共振器來達到濾波的效果。
在實驗方面，本研究成功研製出結合聲子晶體反射結構之雙頻共振器及濾波器，在頻率設計上，其實驗結果與數值模擬相當吻合；在包含兩相異共振腔的雙頻共振器，量測到兩相異之共振頻率，分別為158.29 MHz及164.45 MHz，驗證了共振腔長度與共振模態之頻率的關係；在階梯式濾波器方面，實驗結果亦如預期般，量測到一頻率通帶(bandpass)，中心頻率為159.17 MHz，頻寬約為0.11 MHz。

關鍵字

板波共振器 ； 板波濾波器 ； 聲子晶體 ； 頻溝 ； 有限元素法 ； 品質係數

並列摘要

Phononic crystal (PC) is composed of different materials periodically. One of the most important phenomena of PC is the band gap. Band gap is the frequency space that elastic wave could not propagate through the structure. The resonant phenomena of dual frequency resonator and bandpass filter using PC gratings are studied by numerical simulation and fabrication in this thesis.
The dispersion relations of phononic crystals were calculated by using the finite element method (FEM). To optimize the resonance inside the cavity, the effective reflective plane, transmission coefficient and frequency response were obtained through a series of numerical simulations. Beside, the design of ladder type filter is finish from coupling two one-port resonators together.
On the experimental side, both dual frequency resonator and bandpass filter were fabricated. The measured resonant frequencies are in a good agreement with the numerical predictions. In the dual frequency resonator side, two different resonant with different cavity were measured, 158.29 MHz and 164.45MHz respectively. In the ladder type filter side, a bandpass phenomenon is measured, center frequency is 159.17 MHz and bandwidth is 0.11 MHz.

並列關鍵字

Lamb wave resonator ； Lamb wave filter ； Phononic crystal ； Band gap ； Finite element method ； Q factor

參考文獻

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