具黏滯阻尼器或摩擦消能器之非線性滾動隔震系統 之分析研究

Analytic Study on Nonlinear Rolling Isolation System with Viscous or Friction Damper

謝姃馨(Cheng-Hsin Hsieh)

指導教授 ： 吳賴雲

共同指導教授 ： 鍾立來

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02175

摘要

摘 要
一般線性隔震器的隔震週期恰落在近域地震速度脈衝之常見週期內，因此容易造成共振效應而有過大位移量，為解決此問題，本研究提出了具變頻率的隔震器，稱之為非線性滾動隔震系統，並再建立一對應的線性系統，利用數值模擬方法，比較線性隔震系統與非線性滾動隔震系統，對sine波、近域及遠域地震之減振效果。
在非線性隔震器中，質塊以偏心支點梢接於隔震器圓盤上，當支點偏離時，此系統即具非線性的頻率與回復力。非線性系統可輔以黏滯阻尼器或摩擦消能器，藉加裝消能機制提高隔震效果。以Lagrange’s equation進行運動方程式的推導，由自由振動的數值模擬，了解此非線性隔震器的擺盪行為，發現當隔震器的轉角或偏心距較小時，系統接近線性行為，反之，在大轉角與大偏心距下，非線性特性較明顯。
當地表擾動施以共振頻的sine 波，經數值模擬顯示若無消能機制，線性系統將發散，但非線性系統因具非線性頻率，故可避免發散問題。繼而使用黏滯阻尼消能機制，在共振頻之sine波下線性系統不再發散，但非線性系統約只有線性系統之50 %。當調整遠域及近域地震之PGA由0.05到1 (g)，發現隨兩地震的PGA增大，非線性系統的反應小於線性系統的程度就越大，且非線性的隔震效果也越好，線性系統則無此優點。因此，非線性系統輔以黏滯阻尼消能時，不論在sine波、遠域或近斷層地震下，皆能發揮比線性系統更佳之隔震性能。
消能機制採用摩擦消能器時，由遠域與近斷層地震找出的最佳設計參數非常接近。在共振頻的sine波擾動下，線性系統若使用的摩擦參數不夠大，將因共振作用發散，而同樣參數設定下的非線性系統則無共振發散問題。調整遠域及近斷層地震之PGA由0.05到1 (g) 範圍內，線性與非線性系統的位移反應不分軒輊，但隨PGA增大非線性的隔震效果就越好，而線性系統則無此優點。歸納可知，輔以摩擦消能時，雖然非線性系統的反應與線性系統相近，但當近域及遠域地震的PGA越大，非線性的隔震效果優於線性系統的幅度越大，且隔震效果越好。因此，經由適當之設計，本研究所探討之非線性滾動隔震系統實屬可行。

關鍵字

隔震 ； 滾動 ； 非線性 ； 偏心 ； 黏滯阻尼 ； 摩擦消能 ； 結構動力

並列摘要

Abstract
The vibration period of many linear isolation systems are 2 to 3 seconds which is close to the predominant period of near-fault earthquake, and resonance may occur. For this reason, nonlinear isolation systems are developed to avoid resonance. The frequency of nonlinear isolation system is not fixed, so it can keep the structure from resonance. Numerical simulation is conducted for nonlinear isolation system and the corresponding linear system under free vibration, sine wave, far-field and near-fault earthquake. The linear and nonlinear isolations performance of the system due to harmonic and seismic excitations will also be demonstrated and investigated in this study.
In the proposed system, a mass block is pin connected to a set of circular rolling disk. If the pin is connected eccentrically to the center of the disk, the restoring force becomes nonlinear. In addition, energy is dissipated by adding viscous damper or friction damper. The nonlinear governing equation of motion for the eccentric rolling isolation system is derived based on Lagrange’s equation. The isolation frequency as a function of the eccentricity and initial angle will be investigated through free vibration analysis. By the numerical simulation of free vibration, the results show that if the eccentricity or initial angle is small, the dynamic behavior of the system is almost the same as the linear rolling behavior.
When the ground excitation input is sine wave and its frequency equal to the linearized frequency, the numerical simulation results show that if no dissipation mechanism, the linear system will be divergent, but nonlinear systems will be stable because of its nonlinear behavior. When the viscous damper dissipation mechanism is adopted, under resonant frequency of the sine wave, linear isolation system is no longer divergent, but the maximan response of the nonlinear system is only about 50% of the linear system. When the PGA of El Centro and Chi-Chi earthquakes varies from 0.05 to 1 (g), the result shows that the superior of the nonlinear system over the linear system becomes more obvious as PGA increases. Therefore, with viscous damping, the nonlinear isolation system performs better than the linear one in both acceleration ratio and maximum displacement under sine wave, far field under or near fault earthquakes excitation.
When isolation install friction damper, under far field and near-fault earthquake excitation, the best design of friction parameters are very close. Under resonant frequency of sine wave, the response of linear system will be divergent if the friction parameter is not big enough, while nonlinear system is stable and no resonance occurs at same dutam. Then change the PGA of two earthquakes, the range from 0.05 to 1 (g), the result shows that the displacement of the linear isolation system is closer to that of the nonlinear one.With the increases of PGA, nonlinear isolation display the better isolation effect, but linear system don’t have this advantage. Summarized above, with friction damper, the response of nonlinear systems and linear systems are similar, but if the PGA of near-field and far-field earthquakes becomes larger, nonlinear isolation system shows more and more effect than linear system. Thus, by appropriate design, the nonlinear rolling isolation system is feasible in this research.

並列關鍵字

isolation ； nonlinear ； eccentricity ； viscous damper ； friction damper ； rolling ； structural dynamic

參考文獻

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