本計畫將使用提摩新格樑理論及漢彌爾敦原理，以建立受到週期性軸向力作 用之具局部損傷預扭樑的撓曲振動方程式。該預扭樑的運動方程式將在扭轉座標 系下被推導，再使用有限元素法將該耦合之偏微分振動方程式離散成一 Mathieu-Hill型態之具週期參數的線性二階常微分方程式。然後依據 Bolotin的方 法推導出可用以求得定義該參數激發損傷預扭樑結構的參數不穩定性主區域邊 界的特徵值方程式。藉此，用以探討樑之扭角、損傷位置、損傷長度、損傷程度 係數及穩態軸向力對樑不穩定性區域的影響。計畫中同時將考慮四種典型的固定 -自由樑、銷接-銷接樑、固定-銷接樑及固定-固定樑，以了解不同邊界條件下該 具局部損傷預扭樑的參數不穩定性表現。 The lateral bending vibrations of a twisted beam with localized damage and subjected to a periodic axial load will be established based on the Timoshenko beam theory and Hamilton’s principle. The equations of motion of the twisted beam will be derived in the twist coordinate frame. The partial differential equations of motion are then discretized into a set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type by using a finite element approach. An eigenvalue problem will be formulated to determine the instability regions of the Timoshenko beams with localized damage based on Bolotin’s method. The effects of the twist angle, the damage size, the damage location, the extent of the damage, the axial force and boundary conditions on the parametric instability of the beam will be investigated and discussed.
