轴向运动变长度梁的参数振动
Parameter vibration of an axially moving variable-length beam
熊亚霞 1杜长城1
作者信息
- 1. 西南石油大学机电工程学院， 610500 成都
- 折叠
摘要
研究了一端固定、一端自由的轴向运动变长度梁在长度简谐激励下的参数稳定性。基于Euler-Bernoulli梁理论，利用扩展的Hamilton原理推导了具有轴向运动的悬臂梁的横向振动方程。针对系统的无量纲方程，采用Galerkin方法对系统进行离散，得到具有时变系数的常微分运动方程。应用多尺度方法分析长度随时间简谐变化的悬臂梁的参数振动特性。研究发现，系统存在主共振和组合共振两种失稳形式，并给出了每种失稳形式的失稳临界条件。根据系统的稳定图讨论了长度变化的幅值和频率对轴向运动变长度梁稳定性的影响以及模态阶数对系统失稳类型的影响。结果表明，参与振动的模态越多，系统出现的共振类型就越多。平均长度的增长对系统的失稳起抑制作用，系统的平均长度越小，不稳定区域的面积就越大。最后，通过数值仿真验证了多尺度方法理论计算的正确性。
Abstract
The parametric stability of a cantilever-type beam of an axially moving variable length under the simple and harmonious excitation of length beam is studied. Based on the Euler-Bernoulli beam theory, the transverse vibration equation of a cantilever beam of an axially moving variable length is derived using the extended Hamilton's principle. For the dimensionless equation of the system, the system is discretized using Galerkin's method. And the ordinary differential equation of motion with time-varying coefficients is obtained. The parametric vibration characteristics of the cantilever beam with changing length in harmonic motion are analyzed by multiple scale method. It is found that the system has two types of instability: primary resonance and combination resonance. The critical conditions are given for each instability domain. The influence of amplitude and frequency of length change on stability of the axially moving variable-length beam and the influence of the modal order on the type of system instability are discussed according to stability diagrams of system. The results show that the more modes involved in vibration, the more types of resonances the system has. The instability of the system is inhibited with the increase of the average length. The area of the unstable region increases as the average length of the system decreases. Finally, the correctness of the theoretical calculation of the multiple scale method is also verified through numerical simulation.关键词
变长度梁/轴向运动/多尺度法/参数振动/稳定性引用本文复制引用
熊亚霞,杜长城.轴向运动变长度梁的参数振动[EB/OL].(2025-08-24)[2026-04-03].https://chinaxiv.org/abs/202508.00338.学科分类
力学/工程基础科学/机械学
评论