具週期性柱狀表面平板板波頻溝與共振現象之數值與實驗探討

Abstract

本論文以數值方法以及雷射超聲波實驗探討具週期性柱狀表面聲子晶體平板之頻溝現象以及共振現象。本文使用有限元素法（finite element method, FE）搭配布拉格（Bloch）週期性邊界條件來分析聲子晶體結構之頻散關係及特徵頻率位移場，且利用算例比較有限元素法和平面波展開法所得結果之異同。在數值模擬方面，為了了解柱高對於頻散關係的影響，本文藉由逐步地改變柱高來進行一系列的探討，並發現當柱高為基板厚度的三倍時首次出現全頻溝，且當柱高為基板厚度的九倍時（亦即，圓柱高度加上基板厚度等於晶格常數），全頻溝之寬度最寬。 在實驗方面，本文使用脈衝雷射在基板上激發寬頻之超聲波，並且以氦氖雷射干涉儀及點接觸式壓電探頭來量取縱向及橫向位移，實驗結果顯示量測和模擬結果相當一致;除此之外，在週期性排列的柱子頂端可以發現相當顯著的共振，本文亦對此現象做了詳細的研究和討論。 最後，透過本文的模擬和實驗研究可觀察知，藉由週期性柱狀表面聲子晶體之明顯的共振現象以及高頻震盪的特性，預期此結構可設計作為微液珠混合加速反應時效之應用。

In this thesis, we demonstrate the existence of complete band gaps and resonances in a plate with a periodic stubbed surface both numerically and experimentally. In order to understand the influence of the stubs’ height on the dispersion, a series of numerical calculations are conducted with the help of the finite element (FE) method. Numerical simulated results show that a complete band gap forms as the stub height is about three times of the plate thickness, and as the stub height is nine times of the plate thickness (i.e. the stub height plus the thickness of the plate equal to the lattice constant), the complete band gap is the largest. In the experiment, we use a pulsed laser to generate broadband elastic waves and optical devices as well as point piezoelectric transducers to detect wave signals. Results show that the numerical predictions are in very good agreements with those measured. Moreover, remarkable resonances measured on the top surface of the stubs are found and discussed. In the future, the advantage of this structure is expected to be used in accelerate the reactions of liquids.