移动质量作用下轴向运动悬臂梁振动特性分析

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (3) : 102-105.

论文

移动质量作用下轴向运动悬臂梁振动特性分析

刘宁；杨国来

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Vibration property analysis of an axially moving cantilever beam with the effect of a moving mass

LIU Ning, YANG Guo-lai

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摘要

将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统，推导了轴向运动梁的振动方程，采用修正的Galerkin法离散求解该偏微分方程，得到以模态坐标表示的二阶时变常微分方程组，通过Newmark-β法对方程组进行了求解。计算结果表明，移动质量载荷主要使梁的一阶模态受到激励，移动质量的大小和运动速度对悬臂梁的振动响应影响较大，在移动质量作用下梁的伸缩运动都处于不稳定状态；在移动质量脱离悬臂梁后，梁的轴向收缩运动使得梁的瞬时振动频率不断减小，振动位移逐渐衰减，而振动速度逐渐增大，梁的运动处于不稳定状态，伸展时梁的自由振动规律相反。

Abstract

The projectile-barrel launching system is simplified as an axially moving cantilever beam system under the effect of a moving mass. The vibration equation of the axially moving beam is derived. The modified Galerkin’s method is employed to truncate the governing partial differential equation of the translating beam to a set of second order time-varying ordinary differential equations. Then the equations are calculated based on Newmark-β time integration method. The results show that the first order mode of beam is inspired by the moving mass. The magnitude of the moving mass and its moving speed have an important effect on the beam vibration response and the beam shows instable vibration state in spite of constricting or extending. After the moving mass disengages the constricting beam, the beam instantaneous vibration frequency and vibration displacement are decreased while the vibration speed are increased and the movement of the beam is in the instability state too. However, while the beam are extending, the unrestricted vibration rules of the beam are reverse.

导出引用

刘宁;杨国来. 移动质量作用下轴向运动悬臂梁振动特性分析 [J]. 振动与冲击, 2012, 31(3): 102-105

LIU Ning;YANG Guo-lai. Vibration property analysis of an axially moving cantilever beam with the effect of a moving mass[J]. Journal of Vibration and Shock, 2012, 31(3): 102-105