本計畫將使用提摩新格樑理論及漢彌爾敦原理，以建立受到一週期性軸向壓 力之自旋預扭樑的撓曲振動方程式。並在轉動扭轉座標系下推導該預扭樑之運動 方程式，再使用有限元素法將運動方程式離散成以時間為自變數之陀螺儀型態常 微分方程式，以進行動態分析。計畫中考慮受到週期性變動軸向壓力作用下自旋 預扭提摩新格樑的參數不穩定性， Mathieu-Hill 型態之具週期參數的線性二階常 微分運動方程式將被形成以探討樑之預扭角、幾何參數比、轉速及穩態軸向力對 該系統的不穩定區域的影響。咸信本計畫的分析模型將有助於預扭樑的參數分 析，以更加了解預扭樑與動態行為有關的各種參數對其撓曲振動參數不穩定性的 影響。
Using the Timoshenko beam theory and applying Hamilton’s principle, the present study will establish lateral bending vibrations of a spinning pretwisted beam subjected to a harmonically time-dependent compressive axial force. The equations of motion of the twisted beam will be derived in the rotating twist coordinate frame. The finite element method will be employed to discretize the equations of motion into time-dependent ordinary differential equations with gyroscopic terms. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type will be formed to investigate the influence of twist angle, aspect ratio, rotational speed and axial force on the parametric instability of the beam. It is believed that the present model is valuable for the parametric studies to understand better the various dynamic aspects of the twisted beam affecting its vibrational stability behavior.
