轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (5) : 135-138.

论文

轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应

丁虎1，陈立群1,2

作者信息 +

Steady state response of nonlinear vibration of axially accelerating viscoelastic rayleigh beam

DING Hu1，CHEN Li-qun1,2

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摘要

研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法，构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件，分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程，以验证近似解析方法分析。通过数值算例，分析了系统参数对稳态响应曲线的影响。

Abstract

The sub-harmonic resonance of axially accelerating nonlinear viscoelastic Rayleigh beams are investigated via an approximate analytical method with differential quadrature method verification. The mathematical model of transverse vibration of deformations infinitesimal beams is established by calculus of variations. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The solvable conditions of parametric vibration for sub-harmonic resonance are established via the methods of multiple scales. Therefore the steady state periodic response is presented for accelerating viscoelastic Rayleigh beams with simple supports boundary conditions. Numerical examples show the effects of the nonlinear coefficient and the viscoelastic coefficient on the steady state response are studied individually. The differential governing equation for transverse vibration of an axially moving slender Rayleigh beam is numerically solved via differential quadrature method. The numerical calculations confirm the analytical results. Numerical examples demonstrate that the approximate analysis results are with rather high precision.

导出引用

丁虎;陈立群;. 轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应[J]. 振动与冲击, 2012, 31(5): 135-138

DING Hu;CHEN Li-qun;. Steady state response of nonlinear vibration of axially accelerating viscoelastic rayleigh beam[J]. Journal of Vibration and Shock, 2012, 31(5): 135-138