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