含集中参数弹性梁振动特性解析与实验识别

Analytical Study and Modal Identification Experiment on Free Vibration of Beams Carrying Concentrated Masses and Springs

基于Laplace变换推导出含集中质量与集中刚度弹性梁的振型函数和典型边界条件对应的频率方程,针对有一个集中质量与一个集中刚度的悬臂梁,求解出其固有特性,并利用基于自然激励技术(natural excitation technique,简称NExT)的特征系统实现算法(eigensystem realization algorithm,简称ERA),即NExT-ERA法对相应结构系统进行了模态识别。通过对比解析结果和实验结果,分别讨论了集中质量与集中刚度大小变化和位置变化时对梁振动特性的影响,得出了集中质量和集中刚度在悬臂梁上位置和大小变化时,悬臂梁固有频率的相应变化规律,为工程中具有集中质量和集中刚度等直弹性梁的振动分析方法和集中参数布置设计提供了参考。

The mode shape functions of the elastic beams with concentrated mass and stiffness and their frequency equations under typical boundary conditions are derived with Laplace transform.Using these equations,the inherent characteristics of a cantilever beam with a spring and lumped mass are obtained.Then,its modal parameters are recognized using the NExT-ERA(eigen system realization algorithm based on the natural excitation technique)method.The analytic and experimental results show that modal parameters change with the stiffness and location of the mass and spring.