中间约束轴向运动梁横向非线性振动

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (5) : 142-145.

论文

中间约束轴向运动梁横向非线性振动

赵小颖1, 李彪2, 丁虎1, 陈立群1,3

作者信息 +

Nonlinear transverse vibration of an axially moving beam with an intermediate spring constraint

ZHAO Xiaoying1,LI Biao2,DING Hu1,CHEN Liqun1,3

Author information +

文章历史 +

摘要

聚焦于中间弹性约束对轴向运动梁横向非线性振动的影响。应用哈密顿原理，建立带有中间弹簧支撑的轴向运动梁的动力学控制方程。通过Galerkin截断方法数值计算了简支边界梯型截面轴向运动梁的固有频率，并数值计算得到梁的稳态响应。着重讨论了中间约束弹簧的刚度、系统的轴向运动速度、不同Galerkin截断阶数对系统固有频率、非线性受迫振动稳态响应的影响。研究发现，中间约束弹簧显著改变轴向运动梁的横向振动特性，而且轴向运动的速度能够改变中间弹簧对系统横向振动的影响。

Abstract

Here, nonlinear vibration of an axially moving beam with an intermediate spring support was studied. With Hamilton’s principle, its partial differential dynamic governing equation was established. Natural frequencies and steady-state responses of the beam with trapezoid cross-section and simply supported boundaries were numerically computed by means of Galerkin truncation method. The effects of intermediate spring stiffness, beam axially moving speed and Galerkin truncation orders on the system’s natural frequencies and nonlinear forced vibration steady-state responses were discussed. The numerical results showed that intermediate spring significantly affects transverse vibration characteristics of the axially moving beam; the beam’s axial motion speed can change effects of intermediate spring constraint on transverse vibration of the beam system.

导出引用

赵小颖1, 李彪2, 丁虎1, 陈立群1,3. 中间约束轴向运动梁横向非线性振动[J]. 振动与冲击, 2019, 38(5): 142-145

ZHAO Xiaoying1,LI Biao2,DING Hu1,CHEN Liqun1,3. Nonlinear transverse vibration of an axially moving beam with an intermediate spring constraint[J]. Journal of Vibration and Shock, 2019, 38(5): 142-145

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