非結構物耐震工程的問題之一，在於耐震設計有時會造成非結構物在使用上很大的不便，因此使用者寧可先滿足目前工作的需求，而將耐震防護置於一旁。尤其在各微電子廠房潔淨室中之各項高精度光學平台，其高經濟的生產價值，若無適當的防震措施加以保護，則受地震攻擊時的損失可能無法估計。
本研究提出利用模態分析理論中，建築物每一樓層於反共振頻率處的振動量，會是頻響函數曲線上最小值的特性，做為非結構物新的防震措施設計觀念。藉由調整非結構物的自振頻率至建築物樓板的反共振頻率處的做法，在地震來臨時，將可大幅降低非結構物的振動量。因此只要配合少量的安全措施，便可提高其耐震能力，達到保護該物的目的。
首先推導一般動力系統的反共振頻率，再將其推廣至剪力房屋模型，並經由樓層頻響函數證實理論推導的正確性。應用反共振頻率的觀念設計非結構物的防震措施，則可以樓板反應譜確認其適用性。進一步應用簡化模態分析法及振態值迴歸法，配合模態疊加計算可得既有建築物內低階反共振模態的頻率值，藉此可提供設計非結構物防震措施時必要的參考資訊，簡化複雜的模態分析運算。
對於剪力房屋反共振頻率一般特性的研究，主要可得下列幾點結論：
1. 視非結構物質量為系統質量之一部份時，反共振頻率隨非結構物質量增加而降低，但其改變率並不明顯；而當反共振頻率與自振頻率十分接近時，會產生峰谷消去效應，而使結構反應受到抑制。
2. 當結構柱因地震作用而產生降伏現象，若結構柱之彈塑性剛比小於0.5時，則樓板反共振頻率的改變率均小於10%；而此時非結構物反應的動力放大係數則與彈性反應時十分相近。
3. 剪力房屋受土壤結構互制作用時的結構反應，可經由修正模態分析法求得，並以曲線擬合法模擬複雜的土壤結構互制係數後，可推導建築物於土壤結構互制作用下各樓層的反共振頻率。
4. 土壤結構互制對樓板反共振頻率的影響，方型基礎版較圓型基礎版為大；而不同的土壤剛度變化，僅建築物各樓層的第一個反共頻率，因系統互制作用軟化而產生降低的現象，對於高階反共振模態之影響並不明顯。

One of the reasons that earthquake protection of nonstructural elements has not been successful is because current protection methods often interfere with their usage. It will make, especially, the equipment layout in the clear room of microelectronic plants out of control after an earthquake, and will result huge economic losses.
This dissertation presents a new approach for seismic protection. Because vibration will be minimum at the anti-resonance frequency (ARF) on the Frequency Response Function (FRF) curve in the theory of modal analysis. Nonstructural elements’ natural frequency can be tuned to ARF by adjusting their support condition and the vibration during earthquake will be reduced to a minimum value.
For shear-type building structures, derivation of ARF is demonstrated in this research. As verified through the floor response spectrum of a structure under earthquake motions, the ARF protection approach indicates an effective method for reducing the seismic motion of a SDOF system on a building floor. By using effective modal analysis and mode shape regression, the first few mode of ARF in existing buildings can be found with partial measurements.
Briefly, the main results obtained in this research to shear type building show that:
1. The influence of mass ratio between nonstructural elements to supporting floor has revealed a certain rule of thumb concerning the usage of ARF in seismic application.
2. The change of ARFs in structure and nonstructural elements’ response when inelastic behavior occurs are investigated. Both items change little when structural column yielded.
3. A modal analysis of a shear-type building under Soil-Structure Interaction (SSI) is performed to derive the Modal SSI Matrix. A method to curve fit the complicating correction matrix is proposed, and it can simplify the computation work for the ARF of building floors.
4. A sensitivity study of ARF under the influence of different SSI was found that shear wave velocities have more influence on the first mode ARF and less influence on the higher ARF modes.

封面
目錄
摘要
Abstract
誌謝
目錄
表目錄
圖目錄
符號說明
第一章 緒論
1.1 研究動機與目的
1.2 研究方法
1.2.1 防震觀念
1.2.2 研究方法
1.2.3 研究可行性
1.3 文獻回顧
1.3.1 非結構物受力行為
1.3.2 非結構物耐震補強
1.3.3 反共振頻率
1.4 研究內容
第二章 反共振頻率理論
2.1 動力學理論
2.1.1 多自由度系統
2.1.2 剪力房屋於地震作用之反應
2.2 分析驗證
2.2.1 模型數值分析
2.2.2 頻響函數驗證
2.3 防震措施設計
2.3.1 防震措施
2.3.2 樓板反應譜分析
2.4 小結
第三章 既有建築物之反共振頻率
3.1 簡化模態分析法
3.1.1 減少自由度
3.1.2 疊加分析
3.2 部分量測
3.2.1 振態迴歸
3.2.2 數值與試驗分析
3.3 小結
第四章 樓皮反共振頻率特性
4.1 質量影響
4.1.1 質量改變
4.1.2 防震設計應用
4.2 剛度影響
4.2.1 反共振頻率變化
4.2.2 非結構物反應
4.3 小結
第五章 土壤結構互制之影響
5.1 文獻回顧
5.2 理論
5.3 驗證
5.3.1 曲線擬合
5.3.2 反共振頻率
5.4 案例分析
5.4.1 基礎版及土壤剛度之影響
5.4.2 高寬比之影響
5.5 小結
第六章 結論
6.1 結論
6.2 後續研究
參考文獻
自述
其他

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