本研究設計一單擺調質減振器Pendulum Tuned Mass Damper (PTMD)，懸掛於二維振動剛體下方，此減振器係以一扭矩彈簧及拉伸彈簧與主體連接，提供該單擺減振器兩個自由度的運動，以抑制主體之振動。本系統之主體 (振動剛體) 兩端係以非線性彈簧支撐，用以模擬非線性振動。本研究設計的PTMD，除了其質量、兩個自由度的彈簧係數之外，還有減振器擺放的位置也一併考慮之，以達到系統之最佳減振效果。吾人利用時間多尺度法 (Method of Multiple Scales) 將非線性運動方程式，分成兩個不同的時間尺度，找出系統各自由度之振動頻率，以尋求發生內共振的條件。並藉由本文提出之3-D內共振等值線圖 (Internal Resonance Contour Plot) 的觀念及Fixed Points 頻率響應 (Fixed Points Frequency Response) 的分析，同時分析PTMD的多種參數，以找出避開內共振且大幅減少主體振幅的PTMD組合。最後並以數值模擬驗證本研究的正確性。 This study examines the effects of pendulum tuned mass damper (PTMD) on a nonlinear vibration system. A novel approach is proposed in which an internal resonance contour plot (IRCP) is used for the analysis of nonlinear dynamic stability. This study considers a vibration system with a planar rigid-body, including plunge and pitch vibration. Both ends of the body are supported by cubic nonlinear springs. The vibration absorber attached beneath is a pendulum tuned mass damper (PTMD) and the mass and position of the absorber are adjusted to optimize vibration reduction. The PTMD is attached to the main rigid body by a set of cubic transverse vibration spring and nonlinear torsional spring. The effects of the hinged springs parameters are also considered. The internal resonance condition for the main rigid body is studied by eigen-analysis. The method of multiple scales (MOMS) is employed to obtain a fixed point solution. This study also uses the Poincare Maps and numerical simulations for comparison. Finally, IRCP with Fixed Point plots are cross-referenced to provide guide-lines to identify the optimal location and the mass for the PTMD with regard to stability and reduced vibration magnitude without the need to alter the framework of the main body.
