考慮地盤特性之最佳摩擦係數設計公式與多項式摩擦鐘擺支承雙向實驗及理論分析

Abstract

本文分成兩部份，第一部份為考慮地盤特性之摩擦係數設計公式，第二部份為多項式摩擦鐘擺支承振動台實驗以及雙向數值分析之理論。 本文第一部分主要探討摩擦鐘擺隔震系統之最佳摩擦係數，首先，將運動方程式轉化為狀態方程式，再經離散化後，轉化為離散時間系統下之狀態方程式，用以求得結構反映。接著，因前人所用之地表加速度為白雜訊，並未顯現出臺灣地盤之特性，故本文以臺灣177個地震紀錄作為地表加速度。本文將結構物分成剛體結構以及非剛體結構，表示其運動方程式，利用狀態空間算出不同條件下的最佳摩擦係數，利用這些資料迴歸出一適用於臺灣之設計公式。最後利用實際案例比較前人之方法與本文提供之公式的優劣，以證明本文設計公式之價值。 第二部分為多項式摩擦鐘擺支承(PFPI)振動台實驗以及雙向數值分析之理論，因為傳統摩擦鐘擺支承容易與低頻之震波發生共振之現象，為改善此問題，學者們發展出PFPI。為證明PFPI之隔震效益，於國家地震中心作相關之實驗，分別以PFPI及FPS作為隔震器，輸入之地表加速度皆為真實地震紀錄之倍率縮放，探討兩者間之差異，PFPI之曲盤高程為多項式函數，其回復力亦是如此，功能有二，其一為抑制位移階段，另一為減緩加速度階段，根據支承位移而有不同功能。而較多分析採用單向分析，但地震並非為單向震波，故推導出雙向分析的理論，並以實驗數據驗證理論準確性，比較單雙向分析結果，發現單雙向分析在加速度方面的誤差較小，在特定範圍內僅使用單向分析即可，但隔震層位移方面，單向分析會嚴重低估位移，因此建議分析位移時，雙向分析是必要的。

There are two parts of study in this paper. The first part is about the design formulas for the optimal coefficient of friction which considers the characteristics of different sites. The second part is about the Polynomial Friction Pendulum Isolators, including experiment on the shaking table, and the theory of bidirectional numerical analysis. The first part aims at the optimal coefficient of friction for the Friction Pendulum System. First of all, the motion equation was transformed into state space equation. Then we could obtain the state space equation in discrete-time system for dynamic analysis. Due to the literature of the optimal coefficient of friction for the FPS being analyzed under white noise, it did not consider the characteristics of different sites in Taiwan, so this paper used 177 records of earthquakes in Taiwan as input. After that, considered the structure system in rigid and non-rigid system with varying structure parameters. And the mean square of absolute structural acceleration had been minimized for obtaining the optimal coefficient of friction. Repeating the optimal process with various structural parameters, the proposed simple design formula was developed by regression of those optimal coefficient of friction from numerical simulations. Finally, we conducted the case analysis to verify the feasibility of the proposed optimal design formulas. The second part is Polynomial Friction Pendulum Isolators, including experiment on the shaking table, and the theory of numerical analysis in bidirection. According to the literature, when the FPS is subjected to low-frequency seismic wave, the FPS might lost its effectiveness. For this reason, some scholars invented the Polynomial Friction Pendulum Isolators (PFPI) for improving this problem. In order to prove the effectiveness of PFPI, there was an experiment about sliding isolation systems using PFPI and FPS as isolators to compare the PFPI and FPS. The restoring stiffness of PFPI is variable. Due to this, in different position of isolators, PFPI can reduce the structural acceleration or suppress the isolator drift. A lot of analysis about isolation is unidirectional, but the earthquake is not only in one direction, so this paper derived the theory of numerical analysis in bidirection and checked its accuracy by the result of the shaking table tests. Comparing numerical analysis in unidirection and bidirection, the results showed us two things, one thing is that unidirectional simulation can be used to analyze the structural acceleration in particular position of isolators, another thing is that drift of isolators must be analyzed by bidirectional simulation.