樁型地震超材料的隔減振效益：單元晶格分析、設計與試驗

Abstract

近年來地震工程領域開始關注與探討「地震超材料結構(seismic metamaterial structure)」的研發與應用。從左手材料與光子晶體之概念做為起點，延伸到聲子晶體與彈性波傳上的應用，以人造方式(man-made)設計超材料結構中之單元結構，透過週期性排列，以及採用幾何形狀與材料等參數進行設計，當晶體進入頻率帶隙產生局部共振以阻隔特定頻率的入射波，避免結構物與地震波產生共振而破壞。因此地震超材料在並非採用新穎材料的方式下，即可輕易改變超材料所表現之行為，達到控制波傳或能量傳遞之效果，與傳統的地震工程技術相比，既不用進行複雜的建模與動力分析，保護對象也從單一建築物進一步到可以變成指定的範圍。 本論文主要利用有限元素分析軟體COMSOL進行研究與分析。前半部分藉由前人模型的重現，釐清與驗證單元晶格的相關參數分析和理論，以及確立數值模型的建模細節，方能進行樁型單元晶格的設計，以達到地震波最具有破壞力的目標帶隙0-10 Hz。又由頻散圖上超材料共振頻率之解析解顯示了不同頻率下的波傳遞減幅度，且單元晶格發展到全域模型存在有邊界條件無法完全一致的問題，因此針對設計完的超材料分別進行二維及三維的排數分析，作為實驗設計的參考依據。 因地震超材料結構之模擬方式與頻散曲線之計算與過往傳統實驗相比較為特殊，在有限元素軟體中的模擬可能過於理想，缺乏與實際實驗數據之驗證，且從單元晶格發展到全域模型、二維數值模擬發展至三維，處處都有模擬上的灰色地帶。因此論文後半部，希望透過實驗的設計與進行，除了能更加瞭解模擬與實驗上邊界條件與接觸面之設置差異、驗證超材料在縮尺的行為上是否有可信的結果外，探討超材料在工程上的可行性。另外為了能確認樁型超材料的帶隙表現能從二維發展到三維，實驗也針對不同的樁深度，探討並量化其隔減振之效益。並在實驗結束後，提出實驗試體製作與流程之優化建議。

In recent years, scholars have begun to focus and do research on the developments and applications of seismic metamaterial structures which are composed of common material and purposely designed to shield waves at a certain range of frequencies. Compared with traditional seismic engineering technology, it protects a single structure and also designated area from serious structural damage caused by earthquakes. Local resonance occurs when waves at frequencies around and within the band gap propagate to metamaterials, which prevents the propagation of waves and dissipates energy. By reproducing the model results of previous research using finite element analysis software COMSOL, we can verify the related parameter analysis and theory about unit cell and also establish the numerical modeling detail. When we try to apply designed unit cells to the global numerical model, however, it is observed that the boundary conditions of them are partially inconsistent. Moreover, the numerical simulation model might be too ideal and lack practical verification; thus, aiming to understand when and how the mechanism is triggered and the difference of applied boundary conditions of the unit cell and global model, pile-type seismic metamaterials with different height will be tested in a lab-scale experiment under different planned sweeping sinusoidal input motions. The experimental results demonstrate that responses at frequencies within the designed bandgap are significantly reduced up to 80%-90%, which proved the effectiveness and validity of the pile-type seismic metamaterials structure in attenuating pressure waves. More importantly, the prediction accuracy of the numerical simulation results can be further verified, and full-scale model and field test will be further discussed and schemed.