大运动曲梁应力刚化效应特征值分析  

Eigenvalue analysis of the stress stiffening effect for a curved beam with large rigid motion

作　　者：张建书[1] 芮筱亭[1] 顾俊杰[1] 

机构地区：[1]南京理工大学发射动力学研究所,江苏南京210094

出　　处：《振动工程学报》2016年第5期779-786,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11102089);江苏省研究生培养创新计划基金资助项目(CXZZ12-0177)

摘　　要：从连续介质力学非线性位移-应变关系出发,导出计入应力刚化效应的柔性梁变形能表达式。利用哈密顿变分原理和浮动框架有限元方法(Finite Element Method of Floating Frame of Reference,简记为FEMFFR)导出了匀速转动非惯性系中曲梁的动力学方程。通过数值仿真分析了曲梁的旋转软化(Spin Softening)和应力刚化(Stress Stiffening)效应,并与ANSYS软件仿真结果进行了对比,从结构动力学特征值角度验证了基于连续介质力学非线性位移-应变关系为高速旋转曲梁引入应力刚化效应的方法的正确性。由于曲梁结构不再像直梁结构那样拥有独立的纵向和横向振动模态,为此讨论了改进的Craig-Bampton模态综合法在一般运动曲梁系统中的应用及其缩减策略,为利用浮动框架有限元方法建立满足基于小变形假设的高速旋转柔性曲梁动力学模型提供了参考。Based on the nonlinear relationship between the deformation and the strain of elastic flexible bodies, the expression of the potential energy of a deformed flexible beam is derived. The effect of stress stiffening is accounted for in the potential ener- gy expression. The dynamic equation of a curved beam undergoing uniform rotation and small deformation in a non-inertial co- ordinate system is deduced by using the Hamiltonian variation principle and the finite element method of floating frame of refer- ence （FEMFFR）. The spin softening and stress stiffening of the curved beam is numerically analyzed by using the deduced dy- namic equation. The numerical results are compared with those obtained from the software of ANSYS. From the point of view of eigenvalue problem in structural dynamics, these results validate the method to take into account the stress stiffening effect by using the nonlinear relationship between the deformation and the strain of elastic flexible bodies. For a curved beam, the ax- ial and transversal vibration modes are not independent, which is not the case for a straight beam. Thus, the application of the modified Craig-Bampton modal synthesis method, as well as its reduction strategy, is discussed for the dynamic simulation of a curved beam. Meanwhile, the differences between the ways to take into account the stress stiffening effect in the case of a curved beam with a general motion and that with a uniform rotation are pointed out. The simulation results and discussion lay a foundation for the modeling and analysis of high speed rotating beam system dynamics under small deformation by using the FEMFFR.

关 键 词：多体系统动力学 曲梁 浮动框架有限元法 应力刚化 模态综合法 

分 类 号：O313.7[理学—一般力学与力学基础]