旋转Rayleigh梁动力学性能的研究  

DYNAMIC CHARACTERISTICS OF SPINNING RAYLEIGH BEAMS

作　　者：钱新[1] 杜星文[1] 

机构地区：[1]哈尔滨工业大学复合材料与结构研究所,哈尔滨150080

出　　处：《力学学报》2011年第3期635-640,共6页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：采用广义Hamilton原理推导了旋转Rayleigh梁在重力作用下的运动方程,研究了简支-简支边界条件下旋转Rayleigh梁的动态特性,指出并证明文献中所推导的运动方程缺失了一个由离心力引起的陀螺效应项.理论分析和数值模拟了激励频率、陀螺效应、转动惯量、长细比对涡动频率、临界速度和模态振型的影响.结果表明,正向涡动频率随着激励频率的增加先增加后减小,而反向涡动频率则随着激励频率的增加一直减小;旋转Rayleigh梁有着无限多阶正向和反向临界速度;正向涡动频率总是大于同阶的反向涡动频率.This paper derives the motion equations of the spinning Rayleigh beam under gravitation using the extended Hamilton principle and investigates the dynamic characteristics of spinning Rayleigh beam under a hinged-hinged boundary condition.The present equations show that an important gyroscopic term induced by centrifugal force is missing in similar equations in the literature,but this term is indispensable in the modeling and analysis of spinning beams.The influences of rotary inertia,spinning speed,gyroscopic effects,slenderness ratio on whirling frequencies,whirling modes and critical speeds are investigated in detail using analytical and numerical methods.The results show that the forward whirling speed increases up to the critical speed,and then decreases with the spinning speed;the corresponding backward whirling speed decreases the spinning speed.Each forward whirling speed is higher than the corresponding backward whirling speed.For a spinning Rayleigh beam,there are infinite-dimensional forward and backward critical speeds.

关 键 词：旋转Rayleigh梁 涡动频率 临界速度 陀螺效应 

分 类 号：O347.6[理学—固体力学]