臺灣博碩士論文加值系統

地震超材料透過自然界不存在之現象達到抗震之效果，其現象為帶隙，然而帶隙頻率範圍之上下邊界所表現之波傳現象有所不同，因此本文探討上述兩邊界所產生不同波傳現象之物理意義，並利用此一機制設計超材料，接著利用超材料衰減地震波中最具有威脅性，「雷利波」。由於在眾多文獻中，皆將土壤視為等向性，因此為了更貼近現實，將基材延伸至橫斷面等向性，其自然界中沉積岩即為橫斷面等向性材料。本文透過理論推導雷利波與超材料耦合後之頻散關係，再藉由有限元素軟體對單元結構進行掃頻並驗證理論解，接著利用其結果分析比對雷利波於等向性及橫斷面等向性材料之差別，其中發現橫面等向性中的彈性模數C13、C33及C44皆會影響帶隙寬度，且C13及C44所影響之趨勢與C33相反，其帶隙寬度主要是由帶隙上邊界控制，而帶隙下邊界之共振頻率則不會有所影響，因此利用超材料於任意土壤，只須注意上邊界之變化。最後建立半無限域模型模擬，其雷利波於等向性及橫斷面等向性材料之波傳行為，皆如理論所預測。

Seismic metamaterials can have earthquake resistance effects by utilizing the concept of band gaps. The behavior of wave propagation at a frequency within the bandgap can be substantially different. This thesis investigates Rayleigh wave phenomena and exploits the bandgap mechanism to design metamaterials. The half-space is taken to be transversely isotropic, in a simulation of a type of surface wave in the seismic ground motion of the Earth. Firstly, we derive the dispersion relation based on the classical theory of waves, which is verified by carrying out numerical simulations based on finite element calculations (COMSOL Multiphysics). The objective of this work is to explore the differences between Rayleigh waves propagating in a medium with isotropy and transverse isotropy. It is found that different values of elastic moduli C13, C33, and C44 in transversely isotropic solids affect the upper boundary of the bandgap, thus the width of the bandgap and the effect of C13 is similar to that of C44, while that of C33 will exhibit opposite behavior ; meanwhile, the lower boundary of the bandgap remains unchanged. Lastly, we perform 2D finite element simulations to demonstrate the performance of effects on the propagation of Rayleigh waves in a transversely isotropic domain, and the results are in good agreements with theoretical predictions.

中文摘要 i
Abstract iii
誌謝 xv
目錄 xvi
表目錄 xviii
圖目錄 xix
第一章 緒論 1
1.1 文獻回顧與相關研究 1
1.2 研究動機 4
1.3 論文簡介 4
第二章 局部共振與波傳理論 7
2.1 局部共振 7
2.2 彈性波傳理論 8
2.2.1 地震波簡介 8
2.2.2 波傳於等向性材料之理論與推導 10
2.2.3 雷利波於等向性材料之簡介與推導 14
2.2.4 雷利波於橫斷面等向性材料之簡介與推導 21
第三章 混合雷利波於等向性材料分析與模擬 26
3.1 混合雷利波於等向性材料之頻散關係推導 29
3.2 離散模型分析 37
3.3 連體模型模擬與分析 44
3.3.1 單元結構介紹 44
3.3.2 頻散圖之分析 46
3.3.3 數值模擬 51
第四章 混合雷利波於橫斷面等向性材料分析與模擬 61
4.1 混合雷利波於橫斷面等向性材料之頻散關係推導 61
4.2 連體模型模擬與分析 69
4.2.1 頻散圖之分析 69
4.2.2 數值模擬 76
第五章 結論與未來展望 89
5.1 結論 89
5.2 未來展望 91
參考文獻 93
附錄A : 波傳於橫斷面等向性材料之理論與推導 99
附錄B : 布洛赫定理(Bloch’s theorem) 103
附錄C: 布里淵區(Brillouin zone) 104

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簡廷宇、黃瑜琛、吳逸軒、李冠慧、翁崇寧、陳東陽，新型態外部隔減震技術¬¬-地震超材料之設計與分析，中國土木水利工程學刊，接受發表，2019。


寧彥傑，具負等效質量慣性矩之微極彈性模型設計，成功大學土木工程學系碩士論文，2016。

吳逸軒，寬頻帶地震超材料設計與模擬，成功大學土木工程學系碩士論文，2018。