on extending the concept of double negativity to shear wave

本論文主要將雙負性質(Double negativity)的現象應用在剪力屋架上隔離剪力波。本文所使用的方法是利用結構動力的材料性質及波傳的特性，解特製的剪力屋架模型。此剪力屋架模型將置入一內結構體，當外來彈性波的頻率略大於內結構體的局部頻率而產生局部共振時，此剪力屋架模型會產負等效質量(及負等效模數)，此現象讓彈性波無法繼續傳入剪力屋架，達到把地震波隔離的效果。 在計算一維剪力屋架模型時，以單層質量內還有質量(mass-in-mass)的結構體為單位，用結構動力中解運動方程式可計算出無窮排列的剪力屋架之各層等效質量，而發生負等效質量的範圍與置入的內結構體質量有關。 用彈性波於固體中的波傳理論一樣可以得到相同的頻散關係和結果。 不論是從結構材料方面或是波傳理論探討，都會得出負等效質量或負等效模數。但等效質量和等效模數應同時為正值或是同時為負值；也就是雙負性質。而雙負性質的材料會使波傳前進的方向與能量傳遞的方向相反，換言之，特定頻率的地震波無法傳入有雙負性質的剪力屋架，使結構體就像一個反射器。期望未來可應用在地震工程上。In this paper, we use the characteristic of double negativity to the shear building, isolating it from shear wave. We use the method of dynamics and wave propagations and solve the shear building model. We considered every one floor as a unit and build a inner manmade structure into each unit floor. As the frequency of coming shear wave close to(up to) the local frequency of inner structure brings about the locally resonance, the mass (modulus) of shear building becomes negative. The phenomena keeps the elastic wave from passing through the negative mass(modulus) medium and ensures buildings sustain the shock of waves. We use the mass-in-mass and the equivalent models, calculating the equivalent building mass of each unit by solving the equation of motion. However, the range of arising negative effective mass is related to the mass of inner structure. The equivalent model with effective mass can be represented by one-dimensional elastic solid with a unit cross section, having almost the same dispersive relation and consequences with the discrete mass-in-mass model. o no matter discussing on structure material or wave propagation of the shear building, we get negative effective mass(density) or negative effective modulus. However, it should be either both positive mass (density) and modulus or both negative mass (density) and modulus. That is “double negativity”. The material of double negativity makes the energy and propagating of wave point in the opposite direction, so the material act like a reflector. We expect it can be put into practice on the seismic engineering.目錄謝………………………………………………………………………………… I文摘要…………………………………………………………………………… II文摘要……………………………………………………………………………III 目錄……………………………………………………………………………… VI號對照表…………………………………………………………………………VII 第一章 緒論.1 研究目的與動機……………………………………………………… 1.2 文獻回顧……………………………………………………………… 3二章 基本理論和公式推導.1 單層剪力屋架模型………………………………………………… 5.2 多層剪力屋架模型………………………………………………… 6.3 剪力屋架等價模型之連體系統…………………………………… 7 2.3.1 發生負等效質量的範圍………………………………… 9 2.3.2 零等效質量……………………………………………… 9三章 數值計算 3.1 帶入數字計算和比較………………………………………… 10 3.2 能量轉換機制 …………………………………………… 10 3.2.1 能量短暫的存在內部質量中 ………………………… 13 3.3 負等效質量的剪力屋架之動力反應…………………………… 14 3.3.1 可相互變換調配的常數 ………………………………… 14 3.3.2 波隨空間衰減 …………………………………………… 15 3.3.3 內結構質量塊之振幅……………………………………… 16四章 與香港大學做出的原位共振牆做比較 4.1 文獻大綱………………………………………………………… 17 4.1.1 實驗……………………………………………………… 18 4.1.2 理論分析………………………………………………… 18 4.2 文獻結論 ……………………………………………………… 19 4.3 比較結論 ……………………………………………………… 20五章 結果討論與未來展望 5.1 結果討論 ……………………………………………………… 22 5.1.1 負等效質量的結構系統與阻尼器的結構系統差別…… 24 5.2 未來展望與應用 ……………………………………………… 25考文獻 ……………………………………………………………………… 26圖 …………………………………………………………………………… 2