兩段式非線性單擺式質量阻尼器之研發與實驗驗證

Abstract

臺灣位於歐亞板塊和菲律賓板塊間之擠壓地帶，地震活動非常活躍，對於如何減輕結構在地震時的反應為重大研究方向。調諧質量阻尼器（Tuned Mass Damper）是目前廣泛使用的被動控制系統，然而使用線性彈簧作為調頻機制，利用於低樓層建築中，將受到主結構頻率較低，而限制其使用性。另外，調頻範圍也限於單一頻率，在結構遭受損傷致使勁度及自然頻率改變時，將影響控制效果。本研究將研發新型的被動控制系統，稱為兩段式非線性單擺式質量阻尼器（Dual-length Nonlinear Pendulum），基於調諧質量阻尼器的理論與非線性調諧質量阻尼器（Nonlinear Energy Sinks）提供幾何非線性回復力為設計基礎。將調諧質量阻尼器調頻機制，提升為單擺吊裝質量球，利用在擺動中角度變化所帶來的非線性勁度，使調頻範圍不再只受限於單一頻率；將擺幅範圍內，增加使擺長改變的阻擋版機制，使擺長將隨著輸入外力大小的不同，隨之改變兩種長度，期待在中小型地震與大地震中使用不同區段的消能機制，藉此提升此被動控制系統在低樓層建築的使用性範圍。 本研究將此非線性系統之數值模型建立於電腦軟體MATLAB中進行模擬，透過內建求解函數迭代，進而得到精準的模擬成果。由於非線性系統在分析方法選擇上具有限制性，故本研究將系統控制效果以位移控制作為判斷標準，並且以小波轉換呈現頻率以及能量的變化。在數值模擬分析中，施加不同類型的外力，並利用上述分析方法了解此非線性系統在頻率域及時間域所具有的特性，以及提供的控制行為，藉此歸納出最具控制效果的參數。在實驗驗證部分，以一兩層樓之試體，於此試體加裝本研究所研發之阻尼器，利用振動台提供地震力輸入，驗證本研究所研發項目，具有符合期待的控制效果展現。

Tuned Mass Damper (TMD) is one of well-known passive control systems that can effectively reduce structural responses under seismic excitations. However, due to the high fundamental frequency in low-rise buildings, the allowable displacement is insufficient to accommodate excessive responses during severe earthquakes. In addition, the functionality of a single tuned mass damper is limited to tune an individual frequency, leading to overestimated performance while variation of stiffness occurs. Therefore, an innovative passive control system, entitled “Dual-length Nonlinear Pendulum”, is proposed in this study. This pendulum can provide variable resonances during swinging and result in an applicable frequency range. By means of a specific stopper, the length of a pendulum can be suddenly changed to a short one and yield a high-frequency resonance. Then, the energy from earthquakes is more effectively transferred to high frequencies, and the structural responses can be quickly damped out. Therefore, a pendulum with a stopper has higher capability of mitigating structural responses during severe to extreme earthquake events. In this study, the dual-length nonlinear pendulum is developed and experimentally verified for a seismically-excited model building. First, the numerical model of this nonlinear pendulum is established to understand the dynamic behavior and control performance. A series of parametric studies are carried out to explore the effectiveness and functionality of this nonlinear pendulum for a low-rise building (e.g., with a relatively high fundamental frequency). These studies include the instantaneous natural frequency and mode shapes with respect to positions, frequency-domain amplitudes under harmonic excitation, frequency content due to impulsive loads, energy distributions during earthquakes, and seismic performance. Then, a design example is provided in accordance with the parametric studies, and the dual lengths of the nonlinear pendulum are to tune the first and second natural frequencies of a building. Seismic performance of the building with the optimally designed nonlinear pendulum is also numerically evaluated. Moreover, a two-story, shear-type model building is fabricated to experimentally investigate and verify seismic performance of the proposed dual-length nonlinear pendulum. During the test, records from 1999 Chi-Chi earthquake are considered as the ground excitation. Performance of the nonlinear pendulum is also compared to the uncontrolled bare frame building and the building with a tuned mass damper. This nonlinear pendulum exhibits a high ability to reduce structural responses during relatively large earthquakes. As seen in the experimental results, the proposed dual-length nonlinear pendulum has higher performance than the conventional tuned mass damper, in particular when structural degradation occurs or seismic intensity becomes large.