基于旋转软化的柔性梁动力学研究

Dynamics of flexible beams based on spin softening

建立了旋转柔性梁的非线性动力学模型,利用能量法及哈密顿原理导出了耦合的动力学方程,分析了转动惯性、Coriolis力、应力刚化、旋转软化、加速度、横向位移、弯曲刚度等作用效应;通过设置应力刚化及旋转软化等刚度矩阵和编制有限元程序,建立了梁单元有限元模型,对柔性梁在旋转软化状态下的振动模态进行了数值模拟与分析。计算表明:梁的旋转软化导致其沿旋转平面的弯振模态(摆振)频率随转速增大而相对下降,且对第一阶摆振频率的影响最显著,呈现非线性;梁的旋转软化对垂直于旋转平面的弯振频率几乎没有影响,此结果表明了旋转柔性梁动态特性的复杂性,因此在计算旋转柔性梁的振动特性时,必须同时设置平动、转动惯性质量矩阵,才能获得准确结果。此外,梁单元模型与实体单元模型计算结果误差小于等于5%,验证了本文梁单元模型求解方法的准确性。

A nonlinear dynamic model is developed for a rotating flexible beam. The dynamic equations are derived by using the energy approach and Hamilton's variational principle, in which the effects of the rotating inertia, Coriolis force, stress stiffening, spin softening, acceleration, lateral displacement and bending stiffness are taken into account. Then the finite element dynamic model of the beam is proposed and the effects of the stress stiffening, spin softening etc. are set. Numerical simulation of the beam is carried out and show that the spin softening effect of a beam has significant influence on the bending vibration(swing vibration) frequencies of the rotation plane and the influence on the first order swing vibration frequency is the most significant, which exhibits a nonlinear property, and has little influence on the bending vibration frequencies of non-rotation plane. Results obtained further show the complexity of the dynamic characteristics of rotating flexible beams. To calculate the vibration characteristics of a rotating flexible beam, it must also set both the translational and rotational inertial mass matrices in order to obtain accurate results. The accuracy of the beam model and the solution techniques are demonstrated by comparison with solid model results of commercial software, and the errors less than 5%.