考虑集中质量的旋转悬臂梁的动力学建模与频率分析

摘要

The rigid-flexible coupling dynamics and frequency analysis of a rotating cantilever beam with a concentrated mass located in an arbitrary is studied in this paper.Based on the accurate description of non-linear deformation of the flexible beam,the governing equations with the dynamic stiffening terms for this system are derived from both Lagrange′s equations and assumed mode method,taking the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account.For modeling of the concentrated mass,the Dirac delta function is introduced to avoid increasing the degrees of freedom of the system.The chord-wise equation is transformed into dimensionless form in which dimensionless parameters are identified.The effects of the concentrated mass for natural frequencies in chord-wise bending vibration are investigated through numerical simulation.The results show that the first-order natural frequency loci can be lowered by increasing the concentrated mass ratio,and the natural frequencies vary as the concentrated mass location ratio varies.%对考虑集中质量的旋转悬臂梁的刚柔耦合动力学建模和频率特性进行了研究。在精确描述柔性梁非线性变形基础上,利用Lagrange方程和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下,推导出考虑＂动力刚化＂项的动力学方程。利用狄拉克δ函数,将任意位置的集中质量纳入梁的横向振动动力学方程,避免增加系统自由度。引入无量纲变量,对横向振动动力学方程做无量纲化处理,通过数值计算分析集中质量对柔性梁横向弯曲振动固有频率的影响。研究发现,随着集中质量比率的增大,第1阶固有频率轨迹线在下降;悬臂梁横向弯曲振动的固有频率并非随集中质量位置比率单调变化。