三段式考慮摩擦力之非線性軌道式質量阻尼器之研發與實驗驗證

Abstract

臺灣的地震活動十分活躍，因為其位處於歐亞板塊和菲律賓板塊間的交界擠壓地帶，故對臺灣來說減輕結構在地震下的反應是一大研究方向。本研究中採用的是軌道非線性調節質量阻尼器（Track Nonlinear Energy Sink, NES），是目前廣泛使用的被動控制系統之一，其控制方法為一個質量塊在特定的軌道上移動，產生高度非線性的回復力回饋給結構，並可以將結構系統中的能量轉從低模態轉移到高模態中，使整體能量部分導向 Track NES 的控制系統，達到削減結構系統能量的效果進而減少結構系統的反應，相較於只能在單一頻率產生較好效果的Tuned Mass Damper (TMD)而言，可以適用在不同的頻率且能避免離頻效應的發生。 本研究將所設計的 Track NES 加裝在一個五樓結構的頂樓，並使用 Lagrange’s Equation 推導此結構的多自由度系統的運動方程式，將其在電腦軟體 MATLAB 上建立數值模型並進行模擬，探討在不同的軌道係數及質量比下，Track NES 的效能及行為，並綜合考慮不同類型的外力，建立參數選取的適當範圍，以此設計出一個三段式的軌道。 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結構頂樓的位移及加速度作為判斷控制效果的標準，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，藉此歸納出最具控制效果的參數。在實驗驗證部分，以一個五層樓之縮尺鋼構試體，於此試體加裝本研究所研發之三段式非線性軌道式質量阻尼器，利用振動台提供地震力輸入，驗證本研究所研發項目，是否具有預期的控制效果。 本研究研發之三段式非線性軌道式質量阻尼器具有非常良好的控制效果，可以利用不同段軌道所提供的非線性回復力來使系統適應各種不同的外力，相比於空構架來說其效能十分優秀，雖對比起最佳化TMD來說其效果略遜一籌，不過在有關於阻尼器的反應上其效果十分優秀，相較於TMD來說需要較小的位移就能進行消能且不單只能調頻單一頻率，且NES具有將系統低模態轉至高模態之效果，能夠藉由高模態的固有阻尼使其快速將反應降下來。

Taiwan, due to its geographic location, has frequently seismic events. Thus, developing an effective control strategy to mitigate seismic responses is an urgent task. In this research, the main objective is to develop, design, and experimentally verify a track-type nonlinear energy sink (track NES) with three piecewise-continuous track shapes, namely the three-phase track NES. For a track NES, the moving mass can provide highly nonlinear shear forces to the connecting structure and bring the structural energy from low-frequency to high-frequency modes, resulting in better energy dissipations via the structural inherent damping. As compared to the conventional tuned mass damper (TMD), this NES is more adaptive when the detuning effect occurs. In addition, the track NES requires a specific design procedure due to its nonlinearity and mechanical behavior. For example, the equation of motion for a track NES attached on a MDOF structure is derived by the Lagrange’s equation. Then, seismic responses of this structural system are calculated by the ordinary differential equation solver in MATLAB. Before establishing the design procedure, a series of parametric studies are carried out. The ratio between the NES and total structural masses and the coefficient of track shapes are studied against structural performance when subjected to an initial velocity or single-cycle sinusoidal input. As a result, a sequential design procedure of a track NES is finally established to begin with a circle shape around the equilibrium, fourth-order polynomial shape for the second phase, and linear shape for the last phase. Because of the complex behavior, performance evaluation of a seismically excited building with a track NES is mainly focused on the displacement and acceleration responses. To better understand the NES behavior, multiple sorts of excitations are considered in simulation, e.g., pulse-like loadings and earthquake records. Moreover, time- and frequency-domain performance of this structural system is also investigated. The wavelet transform to the structural and NES responses is conducted to explore the target energy transfer. As for the experimental verification, the three-phase track NES is designed and fabricated in accordance with the dynamic characteristics of a five-story, steel-frame, small-scale building. This building with the designed NES is then examined under seismic excitation through shake table testing. Performance of this structural system is then evaluated using the same steps conducted in simulation. As seen in the results, the developed three-phase track NES provides superior performance for seismic mitigation of building structures.