本計畫將使用提摩新格樑理論及漢彌爾敦原理，以建立具局部Kelvin-Voigt 阻尼且受軸向力作用預扭樑的撓曲振動方程式。並在扭轉座標系下推導該預扭樑之偏微分運動方程式，再使用有限元素法將其離散成以時間為自變數之線性二階常微分方程式。二次式特徵值方程式將被形成以探討預扭角、阻尼係數、阻尼段長度及位置、軸向力及邊界條件該預扭樑系統特徵頻率的影響效應。咸信本計畫的分析模型將有助於預扭樑的參數分析，以更加了解與振動表現有關的各種參數對具局部內阻尼預扭樑撓曲振動特性的影響。
Using the Timoshenko beam theory and applying Hamilton’s principle, the present study will establish bending-bending vibrations of an axially loaded twisted beam with locally distributed Kelvin-Voigt damping. The equations of motion of the twisted beam will be derived in the twist coordinate frame. Then, a finite element method will be used to reduce the equations of motion into linear second-order ordinary differential equations with constant coefficients. A quadratic eigenvalue problem of a damped system will be formulated to study the effects of the twist angle, internal damping, size and length of damped segment, axial load and restraint types on the eigenfrequencies of the damped twisted beams. It is believed that the present model is valuable for the parametric studies to understand better the various variables of the damped twisted beam affecting its vibration characteristics.
