旋转FGM圆环形截面柔性梁的振动特性

Vibration characteristics of rotating flexible ring beam made of functionally graded material

工程实际中直升机的旋翼和风力机的叶片等可简化为旋转柔性悬臂梁的动力学问题。针对旋转FGM圆环形截面柔性悬臂梁的横向振动问题,基于Euler-Bernoulli梁理论和Hamilton原理,建立了自由振动时的运动微分方程。对运动微分方程和边界条件进行量纲归一化处理,采用微分求积法对其进行离散化,得到了系统的广义特征方程。分析了旋转FGM圆环形截面柔性梁的前三阶量纲为一的固有频率随梯度指标和不同梯度指标、径长比下量纲为一的固有频率随轮毂量纲为一的角速度的变化关系。数值计算结果表明,在给定某些参数情况下,旋转FGM环形截面悬臂梁的前三阶量纲为一的固有频率随轮毂量纲为一的角速度的增大而增大,第二阶、第三阶量纲为一的固有频率随梯度指标的增大而增大的趋势较为明显。

The helicopter rotor blades and the wind turbine blades can be modelled as a rotating flexible cantilever beam in engineering practice.For transverse vibration of rotating flexible ring beams made of functionally graded material,based on Euler-Bernoulli beam theory and the Hamilton’s principle,the differential equations of motion of the system is derived.Introducing dimensionless parameters and variables,the differential equations and boundary conditions,which are expressed as the dimensionless quantities,are discretized by differential quadrature method,then the characteristic equation of the system is obtained.Finally,the effects of the gradient index and dimensionless angular speed of the hub under different gradient indices and ratios of hub radius to beam length on the first three dimensionless natural frequencies of the rotating FGM flexible ring beam are analyzed.The numerical calculation results show that with some of the given parameters,the first three order dimensionless natural frequencies of rotating FGM flexible ring beam increase with the increase of dimensionless angular speed of the hub,and the second and third order dimensionless natural frequencies increase obviously with the increase of gradient index.