轴向运动Rayleigh梁固有频率的微分求积法  

Natural Frequency Analysis of Axially Moving Rayleigh Beam Using the Differential Quadrature Method

作　　者：汪昌国[1] 王波[1] 

机构地区：[1]上海应用技术学院机械工程学院,上海201418

出　　处：《机械设计与制造》2015年第12期69-72,共4页Machinery Design & Manufacture

基　　金：国家自然科学基金项目(11202136)

摘　　要：轴向运动梁的振动和稳定性问题是振动力学问题研究的重要内容之一,它有着重要的理论和实际意义。研究了轴向运动Rayleigh梁的固有频率。根据广义哈密顿原理建立轴向运动Rayleigh梁横向振动的控制方程。采用微分求积法数值求解两端简支和两端固支边界条件下轴向运动Rayleigh梁的次临界固有频率。数值例子给出了变化梁的弯曲刚度和支撑刚度情况下第一阶和第二阶固有频率和速度之间的关系曲线。通过曲线间的关系可得到:高阶固有频率比低阶固有频率大,固有频率随着刚度系数的增大而增大,并且随着支撑刚度的增大而增大。The problem of vibration and stability of axially moving beam is very important in vibration mechanics, involving theoretical practical meaning. Natural frequencies of axial moving Rayleigh beam are investigated. The general Hamiltonian principle is developed to derive the transverse vibration equations of the axially moving Rayleigh beams. Under the simply and clamped supported boundary conditions, uses the differential quadrature method to calculate the subcritical natural frequencies of the axially moving Rayleigh beams. Numerical examples give the variations of the first and second natural frequencies venus mean velocities for various flexural rigidities and support rigidities, respectively. The results illustrate that natural frequency is bigger high orders than low orders and increases with flexural and support rigidities increases

关 键 词：轴向运动Rayleigh梁 微分求积法 固有频率 广义哈密顿原理 

分 类 号：TH16[机械工程—机械制造及自动化] O343.5[理学—固体力学]