浸液轴向运动板的非线性自由振动和内共振分析

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (18) : 36-42.

论文

张宇飞1，王延庆2,，闻邦椿1

作者信息 +

ANALYSIS ON THE NONLINEAR FREE VIBRATION AND INTERNAL RESONANCE OF AXIALLY MOVING PLATES IMMERSED IN LIQUID

Zhang Yu-Fei 1，Wang Yan-Qing 2， Wen Bang-Chun1

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文章历史 +

摘要

以竖直浸没于液体中的轴向运动矩形板作为研究模型，根据经典薄板理论以及von Kámán非线性几何关系，得到流-固耦合系统的非线性振动微分方程。假定液体为无粘、无旋、不可压缩的理想流体，流体对板的动压力采用速度势函数及Bernoulli方程描述。然后应用直接多尺度法求解系统的非线性偏微分方程，根据可解性条件，获得系统的非线性频率。最后，分析了浸液轴向运动板的1:1内共振及1:3内共振现象，并讨论了系统参数对该流-固耦合系统非线性动力学特性的影响。

Abstract

A vertically moving rectangular plate immersed in liquid is investigated. Based on the classical thin plate theory and von Kámán nonlinear geometrical relationships, the nonlinear vibrational differential equations of the fluid-structure coupling system are derived. It is assumed that the liquid is incompressible, inviscid and irrotational. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The system is solved by applying directly the method of multiple scales to the nonlinear partial-differential equations. Based on the solvable condition, the nonlinear frequency of the system is obtained. The 1:1 and 1:3 internal resonances of moving plate-fluid system are investigated. The effects of system parameters on the nonlinear dynamic characteristics of the fluid-structure coupling system are discussed in detail.

导出引用

张宇飞1，王延庆2,，闻邦椿1. 浸液轴向运动板的非线性自由振动和内共振分析[J]. 振动与冲击, 2017, 36(18): 36-42

Zhang Yu-Fei 1，Wang Yan-Qing 2， Wen Bang-Chun1. ANALYSIS ON THE NONLINEAR FREE VIBRATION AND INTERNAL RESONANCE OF AXIALLY MOVING PLATES IMMERSED IN LIQUID[J]. Journal of Vibration and Shock, 2017, 36(18): 36-42

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