Relating to a dynamic engineering problem of a disc and blade model in a rigid and flexible coupling system , based on Hamilton's variational principle and finite element method, continuous dynamic equations, nonlinear complete coupling, and time dependant finite discrete dynamic equations of a flexible blade rotating around a fixed axis were derived. Influence of the variation of pre-twisted angles and a variable cross-section on the displacement response of a rotating blade tip was discussed. Results show that variation of a pre-twisted angle and the variable cross-section of a blade have some influence on displacement in the plane perpendicular to the rotating plane, resulting in a touch failure in the case of relatively great displacement. Methods and results in this paper can be used to guide the design of pre-twisted angles and variable cross-section blades.%针对工程中旋转柔性叶片系统刚柔耦合动力学问题,基于Hamilton原理及有限元法建立了大范围旋转运动的预扭角柔性叶片系统连续动力学方程及有限维离散动力学方程,研究了柔性叶片预扭角及截面变化对叶片端部位移响应的影响.研究结果表明:柔性叶片预扭角及截面变化对垂直于旋转平面内的横向位移有较大影响,若过大可使叶片发生动静碰擦,研究方法及结果可为预扭变截面旋转叶片设计提供理论参考.
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