本文主要研究由單一撓性桿件使機構具有雙穩態且非線性彈簧的特性，在力矩輸入下的非線性動態特性。設計與製造出一平面機構，利用鋁片挫曲後非線性撓性使機構產生雙穩態，在外部電磁鐵產生的力矩驅動下，量測機構角度狀態，觀察到平面雙穩態撓性機構豐富非線性響應表現，如共振跳躍、單與雙位能井的混沌響應，也透過希爾伯特黃轉換(HHT)分析工具，處理非線性非穩態訊號，以便同時得到時間、頻率、振幅的資訊，HHT在非線性動態特性的分析上非常有幫助。將非線性系統以穩定點局部線性化來視之，則可透過自然振盪響應與頻率響應進行系統參數鑑定，並進行數值模擬與實驗數據比較，以驗證系統方程式模型正確性。由於系統的彈性恢復力矩為遲滯模型，無法用單一函數表示之，故將其模型近似為標準達芬振子，並使用諧波平衡法(harmonic balance)作頻率、振幅與功率分析，此外，配合Melnikov Criterion以分析實驗所得參數空間中，混沌響應不可能產生之區域；對於此平面雙穩撓性機構的動態特性研究，能應用於振動能量回收，利用直流馬達當作發電機，觀察不同驅動頻率與大小的弦波激擾力矩下，對應的動態響應與發電功率的關聯性。

In this thesis, the nonlinear dynamic characteristics of a bi-stable buckled planar mechanism actuated by a moment input was investigated. After designing and manufacturing the bi-stable mechanism, the angle state of actuating rod was measured under the external torque input via the two electromagnets. Rich dynamic behaviors such as chaotic response in single and double potential energy well were observed. This paper also applies Hilbert-Huang Transform (HHT) analysis tools to process nonlinear non-stationary signals and obtain the time, frequency, amplitude information of the original signal in the same time, and try to explain how chaos appears. In order to acquire the values of system parameters, such as moment of inertia and damping coefficient, approximating a nonlinear system by a linear one around the stable equilibrium points in time-domain and frequency- domain was done. After doing the system identification and estimation, the comparison between the numerical simulations and experiment data can be made to check the validity of the system model. In addition, the restoring torque of the system is similar to the hysteresis model and unable to be expressed as the single and explicit form so the one was approximated to the standard Duffing oscillator. Therefore, Harmonic balance method can be applied to analytically predict the influence of parameter variations on the intrawell and interwell oscillations. For a twin-well Duffing oscillator, Melnikov criteria which can predict the possible chaos region in parameter space was applied in this paper. Finally, a bi-stable, torque actuated, vibrational energy harvester (VEH) was made to investigate the relationship between dynamic behavior and the voltage output of the VEH in different frequency and amplitude of the excitation torque.

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