隔震系統以其柔度阻絕地震力之傳輸路徑,卻帶來隔震層相當可觀之位移,消能機制遂不可或缺,阻尼量過猶不及,均無法兼顧結構耐震及隔震層位移之需求。有鑑於此,本文旨在探討隔震系統之最佳消能參數,主要分為兩部分;線性黏滯消能隔震系統部分,單自由度結構經隔震後成二自由度系統,在白雜訊地表加速度之作用下,使結構絕對加速度之均方最小化,從而求取隔震系統之最佳阻尼比。若結構為剛體或無阻尼,從理論推導,求得隔震系統阻尼比之最佳設計公式。若結構具阻尼,從最小化,得最佳阻尼比之一元四次方程式,工程師利用商用軟體,可解之。此外,本文更彙整最佳化結果,製作成設計圖表,供工程師參考。摩擦消能隔震系統部分,將系統以狀態方程式表示,定義出目標函數,利用變分法將該目標函數予以最小化,可得三組方程式與兩組邊界條件,透過方程式與邊界條件,以數值迭代法即可求得摩擦消能系統之最佳化設計參數,並在五組隨機地表加速度下,變換結構參數,並由數值方法求得相應之最佳參數,配合以迴歸分析,從而建立設計公式。最後,以隨機、El Centro及TAP097測站測得之331地震地表加速度驗證本文所提最佳消能參數之可行性,雖然三者均非用以建立公式之設計地表加速度,但以最佳消能參數所設計之隔震系統,其隔震效果與實際最佳之情況,相當接近,結構之加速度比僅微幅上升,而隔震層之位移卻小幅下降。因此,本文所提之最佳阻尼比,實屬可行,可供工程師作隔震系統初步設計之用。
The present study aims at developing optimum theory and design formula to find the optimum design parameter of two types of isolation systems : linear viscous energy dissipated isolation system and friction energy dissipated isolation system. For part of linear viscous energy dissipated system, minimize the mean square of absolute structural acceleration of single degree-of-freedom main system subjected to white-noise excitation, then the optimum design formula of linear viscous energy dissipated isolation system can be obtained. For part of friction energy dissipated system, the objective function is defined as the sum of squared structural absolute acceleration. Therefore, the optimal friction coefficient which minimizes the objective function can be obtained through numerical simulation under the five specific random ground excitations. Repeating the optimal process with various structural parameters, the proposed simple design formula is developed by regression of those optimal friction coefficients from numerical simulations. Finally, after the design formula is obtained, the feasibility is verified through implementing the proposed deign formula into a single-degree-of-freedom building with viscous and frictional isolation system under random, El Centro and 331 (TAP097) earthquakes. Comparing the performances of isolation system designed by two cases, the proposed design formula and directly optimized by each earthquakes, the performances between these two cases are very close. Consequently, the proposed design formula is simple and generally applicable.