摘要
两端固支屈曲梁是同时包含二、三次非线性项的系统。该研究在小初始挠度屈曲下，受基础激励力变化时系统的非线性动力学特性。利用Galerkin方法对屈曲梁的振动方程进行离散，采用变外激励力增量谐波平衡（IHB）法追踪屈曲梁的动力响应，并用Floquent理论对系统的周期解进行稳定性和分岔分析。研究发现，在小初始挠度屈曲下，梁的反对称模态并未被激发；而随着外激励力的变化，系统会发生倍周期分岔和鞍结分岔，导致解的突变。应用IHB法得到的计算结果与应用四阶Runge-Kutta法得到的数值结果吻合。
Abstract
The nonlinear dynamics of a fixed-fixed buckled beam with low initial deflection subject to uniform hamonic base excitation was concerned, which was governed by a coupled nonlinear equation with both quadratic and cubic nonlinearities.The Galerkin method was employed to discretize the governing equation, and the incremental harmonic balance (IHB) method with variable excitation force was used to track the dynamic response of the buckled beam.The Floquet theory was used to analyze the stability and bifurcation of the solution.It is found that at low initial deflection, the anti-symmetric modes cannot be excited,however, period-doubling and saddle node bifurcations will occur and lead to snapthrough of the solution.The results obtained by incremental harmonic balance method agree very well with those by the numerical integration using the fourth-order Runge-Kutta method.
关键词
屈曲梁 /
非线性动力学 /
增量谐波平衡(IHB)法 /
分岔 /
混沌
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Key words
buckled beam /
nonlinear dynamics /
incremental harmonic balance(IHB) method /
bifurcation /
chaos
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肖龙江，黄建亮.
小初始挠度两端固支屈曲梁的非线性动力学分析[J]. 振动与冲击, 2020, 39(6): 161-166
XIAO Longjiang,HUANG Jianliang.
Nonlinear dynamics of a fixed-fixed buckled beam with low initial deflection[J]. Journal of Vibration and Shock, 2020, 39(6): 161-166
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