跃迁系数对旋转Timoshenko梁弯曲振动的影响

Flapwise Bending Vibration of a Rotating Timoshenko Beam with Transition Parameter

在不同梁模型中,轴向力对剪切力的贡献不同,该特性可以使用跃迁系数进行描述.本文讨论了当旋转导致轴向离心力存在时,其跃迁系数对Timoshenko梁弯曲振动的影响.首先推导了含跃迁系数的旋转Timoshenko梁弯曲振动微分方程.然后使用微分变换法(DTM)对弯曲振动微分方程进行求解,得到了系统的固有频率和振型.最后分析了跃迁系数、转速、截面形状、高跨比等参数对系统振动的影响.结果表明,跃迁系数对旋转Timoshenko梁的固有频率和振型均有影响,尤其在高转速、薄壁截面和大高跨比的情况下影响更加显著.

In different beam models,the contribution of axial force to shear force varies,and this characteristic can be described by using transition parameter.This paper studies the influence of the transition parameter on the flap-wise bending vibration of Timoshenko beams when rotational effects induce axial centrifugal force.At the beginning of the study,the flap-wise bending vibration differential equations for the rotating Timoshenko beam were derived,which considered the transition parameter.In the following section,the differential equations were solved by using differential transformation method(DTM).At the same time,the natural frequencies and mode-shapes of system were obtained.In the end,the effects of transition parameter,rotating speed,cross section shape,and height-to-length ratio were discussed.The results show that transition parameter has an impact on the natural frequencies and mode-shapes of rotating Timoshenko beams,with a more significant effect observed at high rotating speed,thin-walled cross section,and large height-to-length ratio.