轴向变速运动弯曲梁的固有频率分析

ANALYSIS OF THE NATURAL FREQUENCY OF AN AXIALLY MOVING BEAM WITH NON-UNIFORM VELOCITY

基于动力刚度矩阵法对轴向变速运动弯曲梁的固有频率进行分析,根据Hamilton原理,推导轴向变速运动弯曲梁的时域控制方程和边界条件,通过傅里叶变换得到频域控制方程和边界条件,求解频域控制方程,并结合位移边界条件和载荷边界条件,建立轴向变速运动弯曲梁的动力刚度矩阵模型;引入Hermite形式的形函数,建立了轴向变速运动弯曲梁的有限元模型。算例中,通过对比现有文献中的结果、有限元模型结果和动力刚度矩阵法模型结果,验证了该文所建立的力学模型,动力刚度矩阵法比有限元法具有更高的精度和效率,分析了轴向变速运动弯曲梁固有频率随着弯曲梁轴向运动速度、加速度、轴向受力、边界条件的变化规律。

An analysis on the natural frequencies of an axially moving beam with non-uniform velocity was conducted using the dynamic stiffness matrix method. The governing equations and force boundary conditions in the time domain were established via Hamilton's principle, and the governing equation and force boundary conditions in the frequency domain were then developed using the Furious Transformation. A dynamic stiffness matrix model for the beam was created by importing the displacement and force boundary conditions, after computing the governing equation in the frequency domain. The finite element model was created using the Hermite shape function. Then the model was evaluated by comparing results from literature, FEM results, and DSM results. It was concluded that DSM was more accurate and efficient than FEM. The relationships between natural frequency and the axial movement's velocity and acceleration, axial load, and boundary conditions were also summarized.