基于时间有限元方法的旋转柔性叶片动力学响应分析

Dynamic Behavior Analysis of Rotational Flexible Blades Based on Time-Domain Finite Element Method

将时间有限元方法引入到柔性多体系统的数值计算中,研究了旋转柔性叶片系统的刚-柔耦合响应问题.首先,基于非线性梁理论,建立了旋转柔性叶片系统的中心刚体-柔性梁模型,构造柔性叶片系统考虑一次近似耦合的Lagrange函数;其次,采用假设模态方法对空间坐标进行离散,建立系统的时间有限元格式;最后,通过数值实验,分析了柔性叶片的动力学响应.该方法直接构造了系统的离散积分格式,并自动保证了该格式是保辛的,因而具有较高的数值精度和稳定性.数值结果表明:时间有限元可以有效地求解旋转柔性叶片系统内低频大范围运动与高频弹性振动之间的刚-柔耦合问题.

The time-domain finite element method was introduced to investigate the dynamic responses of rotational flexible blades. Firstly, the rotational flexible blades were modeled as a classic rigid hub-fiexible beam system. Based on the first-order approximate coupling （FOAC） model, the Lagrangian function for the rotational flexible blades system was derived. Then, with the assumed mode method （AMM）, the time-domain t-mite element scheme was construc- ted. Finally, the dynamic behavior of the rotational flexible blades was analyzed with the time- domain finite element method through numerical simulation. Constructed directly without deri- vation of the kinetic equations, the proposed discrete scheme is naturally endowed with sym- plectic conservation, high computational accuracy and good stability. Numerical results show that the time-domain finite element method can effectively solve the rigid-flexible coupling problem, in which the low-frequency large motion and the high-frequency elastic vibration of the blades are interactive.