浸液轴向变速运动黏弹性板的组合参数共振

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摘要针对浸没于液体中的轴向运动黏弹性板，考虑其速度发生扰动变化，根据经典薄板理论以及达朗贝尔原理，得到该系统的横向振动控制微分方程。假定液体为无粘、无旋、不可压缩的理想流体，流体对板的动压力由板的附加质量来描述。然后采用多尺度法，分析系统的偏微分方程及边界条件。根据可解性条件及Routh-Hurwitz判据，确定系统和式组合共振与差式组合共振的失稳区域。最后，讨论不同参数对系统两种组合共振失稳区间的影响。

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	张宇飞1
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	刘金堂2
	闻邦椿1

关键词 ：轴向变速运动板, 液体, 参数共振, 多尺度法, 黏弹性

Abstract：An axially moving viscoelastic plate immersed in the liquid, having the variable speed, was considered.According to the classical thin plate theory and the d'Alembert’s principle, the governing equation of the transverse vibration of the system was derived.The liquid was assumed as ideal fluid and thus was inviscid, irrotational, and incompressible.The dynamic pressure of fluid on the plate could be described by added plate mass.Then, using the method of multiple scales, we analyzed the partial differential equations and boundary conditions of the system.Based on the solvability conditions and the Routh-Hurwitz criterion, the instability regions for sum-type and difference-type combination resonances of the system were determined.Finally, the effects of different parameters on the instability regions of the two kinds of combination resonance were discussed.

Key words： Axially moving plate with variable speed liquid parametric resonance multiple scale method viscoelasticity

收稿日期: 2017-11-14 出版日期: 2019-04-15

引用本文:

张宇飞1,2，刘金堂2，闻邦椿1. 浸液轴向变速运动黏弹性板的组合参数共振[J]. 振动与冲击, 2019, 38(8): 69-74.
ZHANG Yufei1,2,LIU Jintang2，WEN Bangchun1. Parametric combination resonance of an axially moving viscoelastic variable speed plate immersed in liquid. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(8): 69-74.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I8/69

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