确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应

Dynamic Response of Bending-torsion Coupled Timoshenko Thin-walledBeam under Deterministic Loads

建立了一种普遍的解析理论用于求解确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应。首先通过直接求解单对称均匀Timoshenko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Timoshenko弯扭耦合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单对称Timoshenko薄壁梁的弯扭耦合动力响应,该弯扭耦合梁所受到的荷载可以是集中载荷或沿着梁长度分布的分布载荷。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,井对动力弯曲位移和扭转位移的数值结果进行了讨论。

A general analytical theory was developed in order to obtain the dynamic response of bending-torsion coupled Timoshenko thin-walled beam under deterministic loads. Firstly, the accurate calculation method for free vibration of Timoshenko thin-walled beam was derived by solving the governing motion partial differential equation of monosymmetric uniform Timoshenko thin-walled beam element. Also the orthonormality condition of principal mode of free vibration of Timoshenko thin-walled beam was derived. Then the dynamic response of bending-torsion coupled monosymmetric Timoshenko thin-walled beam under deterministic loads was investigated by using the normal mode method. The loads on the beam may be either concentrated or distributed over its length. Finally the theoretical expressions for the displacement response of Timoshenko thin-walled beam subject concentrated or distributed harmonic loads were obtained and numerical results for the dynamic flexural and torsional displacements were presented and discussed.