轴向受载的Bernoulli-Euler薄壁梁的弯扭耦合动力响应

建立了一种普遍的解析理论用于研究确定性载荷作用下轴向受载的单对称Bernoulli—Euler薄壁梁的弯扭耦合动力响应。首先通过直接求解轴向受载的单对称均匀Bernoulli-Euler薄壁梁单元弯扭耦合振动的运动偏微分方程，给出了计算其自由振动的精确方法，并导出了轴向受载的Bernoulli—Euler薄壁梁自由振动主模态的正交条件。然后利用简正模态法研究了确定性载荷作用下轴向受载的Bernoulli—Euler薄壁梁的弯扭耦合动力响应，该梁所受到的载荷可以是集中载荷或分布载荷。最后假定确定性载荷是谐波变化的，得到了各种激励下封闭形式的解，并针对具体算例讨论了动力弯曲位移和扭转位移的数值结果。

The Bending-Torsion Coupled Dynamic Response of Axially-Loaded Bernoulli-Euler Thin-Walled Beam

A general analytical theory is developed in order to obtain the dynamic response of bending-torsion coupled axially loaded bemoulli-Euler thin-walled beam to deterministic loads. Firstly,the accurate solution method for free vibration of axially loaded Bernoulli- Euler thin-Walled beam is derived by solving the governing motion partical differential e-quations of monosymmetric uniform thin-walled beam element. Also the orthonormality condition of principal mode of free vibration of axially loaded Bernoulli-Euler thin-walled beam is derived. Then the dynamic response of bending-torsion coupled monosymmetric axially loaded Bernoulli-Euler thin-Walled beam to deterministic loads is investigated by using the normal mode method. Tire loads on the beam may be either concentrated or distributed over its length. Finally the theoretic expressions for the displacement response of axially loaded Bernoulli-Euler thin-Walled beam subjected to concentrated or distributed harmonic loads are obtained and numerical results for the dynamic flexural and torsional displacements are presented and discussed.