轴向运动黏弹性梁横向非线性受迫振动

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (12) : 128-131.

论文

轴向运动黏弹性梁横向非线性受迫振动

丁虎;陈立群

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Transverse non-linear forced vibration of axially movingviscoelastic beam

Ding Hu; Chen LiQun

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文章历史 +

摘要

运用微分求积法数值研究不同边界条件下轴向运动黏弹性梁受到简谐外激励的横向受迫
振动稳态响应问题。扭转弹簧铰支的混杂边界条件在一定条件下可以退化为固定边界或者简支边界。将物质导数黏弹性本构关系应用在控制方程的推导中。运用微分求积方法对两端混杂边界的轴向运动黏弹性梁的非线性受迫振动偏微分模型和偏微分－积分模型做数值解，分析横向非线性受迫振动稳态的幅频响应，数值结果表明，混杂边界下，随着扭转刚度系数的增大，主共振稳态响应的振幅将减小；相同激励下，两端简支梁的稳态响应振幅更大；不同边界下两组模型的幅频响应具有相同的趋势，但是偏微分模型的非线性性质较强。

Abstract

In this paper, forced vibration is investigated for axially moving viscoelastic beams constrained by simplesupports with torsion springs via differential quadrature method. Under certain conditions, the boundary conditions with thehybrid supports respectively yield the simply supported or the fixed supported.It is assumed that the excitation is spatiallyuniform and temporally harmonic. The material time derivative is used in the viscoelastic constitutive relation. Thedifferential quadrature schemes are developed for a nonlinear partial-differential equation and a nonlinearintegro-partial-differential equation for the steady-state response. Numerical examples demonstrate the amplitudes of stablesteady-state responses decrease with the constraint stiffness. Numerical examples also indicate that the amplitude predicted
by the fixed supported is smaller than that by the simply supported, and two models yield the same existence condition, butthe amplitude predicted by nonlinear integro-partial-differential equation is bigger than that by nonlinear partial-differentialequation.

导出引用

丁虎;陈立群. 轴向运动黏弹性梁横向非线性受迫振动[J]. 振动与冲击, 2009, 28(12): 128-131

Ding Hu;Chen LiQun. Transverse non-linear forced vibration of axially movingviscoelastic beam[J]. Journal of Vibration and Shock, 2009, 28(12): 128-131