結合不連續慣質與單擺摩擦支承隔震系統於重要設備之初步研究

Abstract

台灣處於歐亞板塊與菲律賓板塊的交界帶，其地震活動十分活躍，經常造成嚴重之經濟損失，亦會對人民性命造成一定程度之威脅，最終危害整體社會之發展，因此台灣對於耐震方面之研究日新月異，以強化建築、橋梁與相關重要設施、設備，以有效減少地震帶來之風險。目前基底隔震是被廣泛用來降低地震反應的控制方法之一，透過安裝隔震器於結構或是設備物底部，改變系統的動力特性延長結構週期，以達到遠離地震主要頻率範圍，降低地震衝擊；然而，有研究學者指出，當基底隔震面臨大地震時，會有使用性及安全性不足的顧慮。 近年來許多學者提出利用轉動慣量的方式，可有效提升系統的有效質量，稱為慣性質量(Inerter，簡稱慣質)，其原理為產生機構兩端相對加速度的控制力，並可將水平的側向力轉換成扭矩，在此將其稱為慣質力。此外，有學者指出慣質可增強系統能量的消散能力。因此，諸多學者針對慣質提出不同性能增強裝置，若將慣質直接應用於隔震系統中，本研究稱其為「全時慣質隔震系統」，可藉由調整慣質力以增加系統之慣性力，且在運動方程式中慣性力之方向與系統運動方向相反，可有效抑制隔震系統位移反應，進而提升隔震系統的性能表現。然而，過去的研究指出，此裝置面臨超越設計地震時會引致過大的加速度反應。 本研究提出結合不連續慣質(discontinuous inerter)與單擺摩擦支承隔震系統，加入有效慣質長度探討其動力行為，在有效慣質長度內時，慣質將與隔震系統同時運動發揮慣質之效能抑制位移反應，若當慣質在超出設計切換位移時，隔震系統將不再帶動慣質轉動，使慣質不再回傳能量於隔震系統進而降低加速度反應，使其在中小地震時充分發揮慣質之特性有效控制系統位移反應，在超越設計地震力時降低系統加速度反應。 本研究的流程如下，首先利用牛頓第二運動定律推導運動方程式，再以拉格朗日法進行驗證，由於系統為非線性系統，利用Runge-Kutta法的概念，將系統每一步時間長做離散處理，利用電腦軟體MATLAB做數值模擬。本研究中設計的部分採用非平穩隨機振動設計方法，主要透過不連續慣質隔震系統與原隔震系統比較，以絕對加速度之均方根進行設計，模擬證明非線性隔震系統於不同地震強度下，其均方根反應控制明顯優於傳統線性隔震系統；再依其結果針對最大考量地震下之隔震層最大位移的平均與標準差進行估計，進而作為隔震系統最大容許位移的基準。接下來利用諧波平衡法(Harmonic Balance Method, HBM)求得非線性系統的頻率-振幅函數(Frequency-Response Function)，藉此獲得不連續慣質隔震系統適用頻率之關係，並比較不同慣質比對隔震系統的影響。接下來透過時間域的分析，將設計完成後之設計參數透過數值模擬證明不連續隔震系統於不同地震強度下，其均方根反應控制明顯優於傳統線隔震系統。接著輸入真實地震力進行數值模擬，比較三種不同的隔震系統進行效能評估。實驗驗證的部分，觀察三種隔震系統在簡諧波以及地震輸入下的動力行為是否符合數值模擬，並且驗證非連續慣質隔震系統之減震性能。

Taiwan, due to its geographic location, has frequent seismic events, often leading to severe economic losses and endangering people's lives. Thus, Taiwan's research on earthquake resistance is advancing rapidly to reduce the risks brought by earthquakes. Base isolation is one of the widely used methods nowadays to mitigate seismic responses of superstructures. Installing isolators at the bottom of the structure or equipment can shift the fundamental frequency of a structural system away from the main frequency of earthquakes and then reduce seismic impact. However, some scholars have pointed out that base isolation may have concerns about usability and safety during severe earthquakes. In recent years, many scholars have proposed the use of rotational inertia, which can effectively increase the effective mass of the system. Its principle is to generate a control force from the relative acceleration at the two ends of the mechanism. Additionally, scholars have indicated that out that the inerter can enhance the system's energy dissipation capability. Due to the above characteristics, many scholars have proposed different performance enhancement devices for the inerter. Applying the inertia force can effectively mitigate the displacement response of the isolation system. However, past research has pointed out that this device may cause excessive acceleration responses when exceeding the design earthquake. This study proposes combining a discontinuous inerter with an isolation bearing system and introducing an effective inerter length to investigate its dynamic behavior. When the displacement is less than the effective inerter length, the isolation layer will carry the inerter. On the contrary, the inerter will detach from the isolation system. This allows the system to effectively control the displacement response during small earthquakes, while reducing the acceleration response during earthquakes exceeding the design earthquake force. The research process is as follows: First, the equation of motion is derived using Newton's second law of motion, and using the Lagrangian method to verify. In the design part, the non-stationary stochastic vibration design method is adopted. The main comparison is made between the discontinuous inerter isolation system and the original isolation system, using the root-mean-square of the absolute acceleration for design. Based on the results, the average and standard deviation of the maximum isolation layer displacement under the maximum considered earthquake is estimated, serving as the basis for the maximum allowable displacement of the isolation system. The harmonic balance method is used to obtain the frequency-response function of the non-linear system and compare the effects of different inerter ratios. Then, through time-domain analysis, the design parameters after completion are numerically simulated to demonstrate that the discontinuous isolation system has significantly better root-mean-square response control than the original isolation system under different earthquake intensities. Real earthquake forces are then input for numerical simulation, and the performance of three different isolation systems is evaluated and compared. In the experimental verification part, the dynamic behavior of the three isolation systems under harmonic waves and earthquake inputs is observed to verify whether it matches the numerical simulations, and the vibration reduction performance of the discontinuous inerter isolation system is verified.