旋转Rayleigh梁的自由振动及失稳特性  

Free vibration and buckling characteristic of rotating Rayleigh beam

作　　者：杨高峰 杜长城[1] 邵永波[2] 熊春 Yang Gaofeng;Du Changcheng;Shao Yongbo;Xiong Chun(Schoo of Mechatronie Engineering,Southwest Petroleum University,610500,Chengdu,China;School of Civil Engineering and Gcomatics,Southwest Petroleum University,610500,Chengdu,China)

机构地区：[1]西南石油大学机电工程学院,成都610500 [2]西南石油大学土木工程与测绘学院,成都610500

出　　处：《应用力学学报》2020年第3期1178-1183,I0018,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11602208);四川省科技计划项目(2019JDTD0017);西南石油大学青年科技创新团队项目(2018CXTD07)。

摘　　要：基于Hamilton原理,采用模态坐标得到了旋转梁在固定参考系及旋转参考系下的时域常微分方程,详细分析了两端简支边界条件下旋转Rayleigh梁自由振动的行波特性及临界转速。讨论了长细比等因素对旋转Rayleigh梁的行波振动频率和临界转速的影响,并给出了不同转速下系统自由振动的典型模态坐标时间曲线。研究发现:旋转Rayleigh梁系统存在一次和二次临界转速,固定参考系中一次临界转速对应于旋转参考系中零特征值失稳点,转速在一次临界转速(低速)附近时系统只发生共振失稳,系统真正的失稳发生在转速超过二次临界转速之后。Based on Hamilton’s principle,ordinary differential equations for modal coordinates in time-domain of the fixed frame and rotating frame are obtained.The traveling wave and the critical speed in free vibration of the simply supported rotating Rayleigh beam are analyzed.The effects of slenderness ratios on vibration frequency and critical speed are discussed.The typical modal coordinate curves in free vibration of different speeds are plotted.It is found that there are first and second critical speed in rotating Rayleigh beams.The first critical speed in the fixed frame corresponds to the zero eigenvalue instability point in the rotating frame.The resonance of the system occurs at first critical speed(low speed).Vibration instability occurs when the speed exceeds second critical speed.

关 键 词：旋转梁 自由振动 临界转速 行波特性 

分 类 号：O32[理学—一般力学与力学基础]