Timoshenko 模型轴向运动梁的横向振动特性分析Ξ.PDF

( ) Journal of Mechanical Strength 2008 ,30 6 :903～906 Timoshenko 模型轴向运动梁的横向振动特性分析 DY NAMICS OF TRANSVERSE VIBRATIONS OF AXIALLY MOVING BEAM FOR TIMOSHENKO MOD EL 杨晓东 　唐有绮 (沈阳航空工业学院 工程力学系 ,沈阳 110136) YAN G XiaoDong 　TAN G YouQi ( Dep artment of Engineering Mechanics , S heny ang Institute of A eronautical Engineering , S heny ang 110136 , China) 摘要 　通过对梁微单元体的受力分析 ,导出 Timoshenko 模型的轴向运动梁横向振动的运动方程 , 并利用复模态分析 方法及半解析半数值方法 , 研究两端铰支条件下轴向运动梁横向振动的振动模态及固有频率 。文中还讨论运动梁前两 阶固有频率随轴向运动速度变化的情况 。最后利用数值算例对 Timoshenko 梁 、Euler 梁 、Rayleigh 梁及剪切梁的固有频率 进行比较 , 分析转动惯量及剪切变形的影响 。 关键词 　轴向运动梁 　固有频率 　Timoshenko 梁模型 中图分类号 　O325 　TH113 . 1 Abstract 　The governing equation of the axially moving beam for the Timoshenko model is derived by using the Newton ’s second law. The complex mode method is applied to the governing partial differential equation and the resulting ordinary differential equation is studied by the semianalytical approach . The transverse vibration modes and their natural frequencies are investigated for the beam on simple supports. The contributions of some parameters , such as axially moving speed , the moment of inertia , and the shear deformation , are discussed respectively , as other parameters are fixed. Some numerical examples are presented to show the comparison of natural fre quencies for four beam models , namely , Timoshenko model , Euler model , Rayleigh model and shear model . Key words 　Axially moving beam ; Natural frequency ; Timoshenko beam mo