樁型拉脹地震超材料之減振研究

Abstract

地震超材料，是一種以結構被動控制之精神所延伸出的一種新型態，其最核心的表徵在於能夠阻隔特定頻率內涵的波傳。地震超材料的理論基礎源自於聲子晶體的觀點並將其應用於固體力學中的波傳問題。地震超材料蘊含之頻率帶隙特性能干擾特定頻率的入射波傳遞進而保護建築物乃至一個城市範圍，然而，因超材料原先的發展是應用於抵擋高頻率的聲波甚至光波，面對結構工程等大尺度物理問題就得面臨許多挑戰，地震超材料之技術發展的最大的瓶頸在於如何在經濟與土地使用空間等綜合考量下去設計出與地震波頻率相互匹配的帶隙。 近年來的研究已經展現出拉脹材料及拉脹結構對於巨大的能量吸收與緩衝有優異的效果，除此之外，亦有許多研究指出拉脹結構本身因其特殊的力學模態特性對於產生出帶隙與加寬帶隙的頻率範圍有潛力，因此，為了能夠達到超低頻率帶隙的需求，本研究將整合樁型地震超材料與拉脹結構的優點去設計出新型態之樁型拉脹結構地震超材料以利更加符合針對低頻率地震波的需求。 在本研究中，首先推導了一維數學模型來解釋與驗證週期性排列結構的行為和性質，並將其布洛赫定理與不可約化布里淵區導入有限元素數值模擬之的邊界條件與波傳假設。並且根據一維數學模型與有限元素法分析結果可以推斷，負波松比材料確實會對帶隙產生影響，因此可以將其視為設計時可納入考量的材料性質。此外，為了更進一步設計出低頻率帶隙之單元晶格，將利用有限元素法軟體計算二維和三維單元晶格的頻散關係，並且為了確保此特殊物理性質存在於固體力學之波傳問題的統御方程式中，將同時使用 ABAQUS 和 COMSOL Multiphysics 來進 行交互比對，從而提高此數值結果的可靠性，以及排除前人們兩種軟體擬合問題。透過參數分析可以發現，針對某些幾何與材料性質之下，拉脹結構之負波松比可以急速加寬帶隙，進而設計出有效之地震超材料。此外，為了確認所設計之拉脹結構具有實際的拉脹特性，本研究使用 3D 列印熱堆疊技術製作出了三維拉脹結構用於測試其波松比性質與幾何推導公式答案一致以利後續最佳化設計。 此外，建立了一系列三維實尺數值模型來研究波傳與帶隙之機制，並評估保護區之位移場和加速度場的折減效果，因這些物理特性是影響結構系統的關鍵因素。並且由數值模擬結果可以發現，局部共振的生成確實是阻止波傳的機制。最後，真實的地震波也會被採納為入射波用以測試拉脹樁型地震超材料之可行性與效益。分析結果表明，這種創新的地震超材料能夠衰減低頻帶隙內的響應，為結構工程領域帶來新的思維。

A seismic metamaterial is an innovative form of passive control technology that can block wave propagation within a particular frequency range. The fundamental spirit of seismic metamaterials is derived from the viewpoint of phononic crystals and is extended to the application of wave propagation in solid mechanics. These metamaterials possess unique properties such as frequency band gaps, which prohibit the passage of incoming waves with frequencies falling within the range of these gaps. However, the research and development of seismic metamaterials are ongoing because achieving a low-frequency band gap with a sensible lattice constant still presents a challenge. Numerous recent studies have demonstrated that auxetic materials or structures can offer protective applications, such as blast and impact energy absorption. Besides, the auxetic structure itself also owns the potential to create band gaps and broaden the width of the band gap. Thus, in order to achieve a low-frequency band gap, this study will utilize seismic pile-type metamaterials as a foundation and integrate an advantageous auxetic structures. In this study, a one-dimensional theoretical mathematical model was first derived to explain the behavior and property of the periodic structure. According to the mathematical model, it can be inferred that the negative Poisson’s ratio material indeed widen the width of the band gap. To further design the unit cell, finite element software was utilized to calculate the dispersion relationship of the two-dimensional and three-dimensional unit cells. To ensure calculating accuracy, both ABAQUS and COMSOL Multiphysics will be used simultaneously to compare results, thereby increasing the reliability of the study and solving the mismatch from previous research. The optimal value of the negative Poisson’s ratio can be determined by analyzing the parameters, and the auxetic structure can be designed. To confirm that the designed auxetic structure exhibits actual auxetic characteristics, a three-dimensional auxetic structure was produced by using 3D printer technology for testing purposes. Moreover, three-dimensional full-scale numerical models were established to study the mechanism of wave propagation blocking and assess the reduction in displacement and acceleration, which are crucial factors for structural systems. Based on the simulation results, the existence of local resonance could be observed and proved that this type of mechanism indeed blocks the propagation of waves. The true seismic events were also set as incoming waves for simulating the actual scenario. The analysis results demonstrate that this innovative seismic metamaterial is capable of attenuating the response within the low-frequency band gap, offering significant benefits to the field of structural engineering.