多激励作用下的矩形薄板横向非线性振动分析

张丹伟 黄建亮

振动与冲击 ›› 2016, Vol. 35 ›› Issue (23) : 174-179.

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PDF(1480 KB)
振动与冲击 ›› 2016, Vol. 35 ›› Issue (23) : 174-179.
论文

多激励作用下的矩形薄板横向非线性振动分析

  • 张丹伟 黄建亮
作者信息 +

Nonlinear dynamics of thin plate subject to multiple force excitations

  • ZHANG Dan-wei,HUANG Jian-liang
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文章历史 +

摘要

利用增量谐波平衡法(Incremental Harmonic Balance method, IHB法)研究在四边简支条件下,薄板在两个横向简谐激励作用下的非线性振动问题。在给出薄板振动微分方程的基础上,利用Galerkin法导出相应的Duffing型非线性强迫振动方程。引入多时间尺度变量 ,其中 是不可公约的非线性系统响应频率,推导了增量谐波平衡法的计算过程。作为算例,给出了不同条件下,由IHB法得到的系统运动的位移响应图、频谱图、相平面图和Poincaré图,得到了板在多激励作用下的准周期运动特性。同时,将IHB法结果与数值方法得到的结果进行对比,两者相吻合,进一步验证了该方法的精确性与有效性。

Abstract

The Incremental Harmonic Balance (IHB) method was used to analyze nonlinear dynamics of rectangular thin plate with four simply supported sides, subjected to the external two-tone transverse harmonic excitation. Based on the vibration differential equation of thin plate, the non-dimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method. Introducing multiple time variables defined as  , in which   were the nonlinear frequencies of responses incommensurable with one another, corresponding calculation process of IHB method was derived. As a numerical example, time histories diagrams, spectrum diagrams, phase diagrams and Poincaré section were presented by IHB method with different excitations, and quasi-periodic motions of the plate which undergo the external multi-excitations were obtained. Meanwhile the results obtained from the IHB method are in good agreement with the results obtained from the numerical integration method.

关键词

矩形薄板 / 非线性振动 / 增量谐波平衡法 / 多激励力作用 / 准周期运动

Key words

rectangular thin plate / nonlinear vibration / Incremental Harmonic Balance method / multiple force excitations / quasi-periodic motion

引用本文

导出引用
张丹伟 黄建亮. 多激励作用下的矩形薄板横向非线性振动分析[J]. 振动与冲击, 2016, 35(23): 174-179
ZHANG Dan-wei,HUANG Jian-liang. Nonlinear dynamics of thin plate subject to multiple force excitations[J]. Journal of Vibration and Shock, 2016, 35(23): 174-179

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