考虑安装面特性参数的悬臂梁固有频率分析

Natural frequency of cantilever beam considering the characteristics of installation surface

为研究悬臂梁安装的接触刚度和摩擦系数对其固有频率的影响,首先采用ANSYSY-workbench软件对悬臂梁建立有限元模型并进行模态分析,导出横向弯曲振动的固有频率和模态振型。同时根据欧拉—伯努利梁理论求解悬臂梁横向弯曲振动方程,得到悬臂梁横向弯曲振动的固有频率及模态振型的数值解,对比有限元分析与理论推导的前6阶模态分析结果,两者的模态振型一致,对应的固有频率相对偏差率最大值为4.15%。对比分析结果说明,运用ANSYSY-workbench软件进一步分析悬臂梁安装的接触刚度和摩擦系数对固有频率的影响是可行的。建立有安装接触面的悬臂梁有限元模型,针对讨论的悬臂梁横向弯曲振动情况,在悬臂梁上下两个接触面设置考虑摩擦因素的两个接触对,分别分析接触面的法向接触刚度和摩擦系数对悬臂梁固有频率的影响,并同时对接触刚度进行了实验研究。仿真与实验结果表明,有安装接触面的悬臂梁固有频率随着法向接触刚度与摩擦系数的增大而增大,且有安装接触面的悬臂梁固有频率小于约束端完全固定的悬臂梁固有频率。

In order to study the influence of contact stiffness and friction coefficient on the natural frequencies of cantilever beam installation,the finite element model of cantilever beam is established by using ANSYS-workbench software,and modal analysis is carried out to calculate the natural frequencies and modal shapes of transverse bending vibration.At the same time,the transverse vibration equation of the cantilever beam is solved according to Euler-Bernoulli beam theory,and the numerical solution of the natural frequencies and mode shapes of the transverse bending vibration of the cantilever beam is obtained.Compared with the first six modal analysis results determined by finite element software and theory,the modal shapes of the two methods are consistent,and the maximum relative deviation rate of the corresponding natural frequency is 4.15%.So it is feasible to use ANSYS-workbench software to further analyze the influence of contact stiffness and friction coefficient on natural frequency of cantilever beam in installation state.The finite element model of cantilever beam with installed contact surface is established.In view of the transverse bending vibration of cantilever beam discussed,two contact pairs with friction factor are set up on the upper and lower contact surfaces of cantilever beam.The influence of the normal contact stiffness and friction coefficient of the contact surface on the natural frequency of the cantilever beam is analyzed,and the contact stiffness is also studied experimentally.The results of simulation and experiment show that the natural frequencies of cantilever beam with installed contact surface increase with the increase of normal contact stiffness and friction coefficient,and the natural frequencies of cantilever beam with installed contact surface are less than the of cantilever beam with completely fixed constraints.