旋转薄壁圆柱壳振型进动的非线性振动特性

NONLINEAR VIBRATION CHARACTERISTICS OF ROTATING THIN-WALLED CIRCULAR CYLINDRICAL SHELL WITH PRECESSION OF VIBRATION MODE

选取在工程上常用的悬臂旋转薄壁圆柱壳为研究模型,首先推导出考虑阻尼的振型进动因子,然后根据Donnell’s简化壳理论建立考虑科氏力,阻尼与几何大变形的非线性波动方程,采用Galerkin方法对波动方程进行离散化,得到模态坐标中相互耦合的三阶非线性微分方程组.应用Runge-Kutta法求解获得非线性幅频特性曲线,分析了不同模态组合下系统主模态(m=1,n=6,k=1)的共振响应.应用谐波平衡法对系统三阶非线性微分方程组解析分析,与数值解比较验证了解析解的正确性和有效性.最后分析了动力系统的运动稳定性.结果表明,节径数n和频率倍数k对于主模态共振响应的影响很小,而轴向半波数m对主共振的影响则相对较大,因此只需选取相邻的两个轴向模态(M=2)即可较为简洁,准确的描述主共振响应;谐波平衡法可以很好的解决三阶微分方程组的非线性问题,并且能够达到较为满意的精度.

A cantilever rotating thin-wall circular cylindrical shell is investigated in this paper. The factor of precession of vibration mode is obtained with considering damping. Based on Donnell＇s shallow shell theory,nonlinear wave equation is derived, in which the effect of Coriolis force, damping and geometric largeamplitude are considered. Coupled third-order nonlinear partial differential equations are obtained through Galerkin method. Different responses of double-modes are eompared with that of single mode. The method of harmonic balance is applied to study the non-linear dynamic response of the third-order nonlinear partial differentiation system. It can be found that the resonance curves obtained with method of harmonic balance can agree with numerical simulation very well,indicating this method is effective with very good accuracy. The stability of motion is also investigated. The result obtained shows that, （1） the effect of circular nodal diameters n and multiples of frequency k on principal mode （m=1 ,n= 6 ,k = 1） resonant response are insignificant but that of axial half waves m is significant. Thus it is better to choose two neighboring axial modes （M=2） to study principle resonant response; （2） the method of harmonic balance can solve third-order nonlinear partial differentiation equations very well and have a good accuracy.