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首页> 外文会议>International Design Engineering Technical Conferences;Computers and Information in Engineering Conference;International Conference on Multibody Systems, Nonlinear Dynamics, and Control >MODAL ANALYSIS TO INTERPRET LOCALIZATION PHENOMENA OF HARMONIC OSCILLATIONS IN NONLINEAR OSCILLATOR ARRAYS
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MODAL ANALYSIS TO INTERPRET LOCALIZATION PHENOMENA OF HARMONIC OSCILLATIONS IN NONLINEAR OSCILLATOR ARRAYS

机译：非线性振子阵中谐波振动解释局部化现象的模态分析

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摘要

This paper investigates localization phenomena in a nonlinear array with N Duffing oscillators connected by weak, linear springs when the array is subjected to harmonic excitation. In the theoretical analysis, the equations of motion are derived for: (1) the physical coordinate system, and (2) modal coordinate system. The modal equations of motion form an autoparametric system, i.e., the excitation acts directly on the first mode of vibration, and the other modes are indirectly excited because they are nonli nearly coupled with the first mode. Van der Pol's method is employed to obtain the solutions of the harmonic oscillations, and then the expressions of the frequency response curves are given. In the numerical calculations, the frequency response curves of the amplitudes and phase angles in the cases of N=2 and 3 are presented. The frequency response curves, obtained in the modal coordinate system, demonstrate that localization phenomena occur in the physical coordinate system when multiple vibrational modes simultaneously appear. When imperfections exist in the N Duffing oscillators, the modal equations of motion do not form an autoparametric system because the external excitation directly acts on all modes. Instead, internal resonances may occur in such systems.
机译：本文研究了非线性阵列的局部现象，该非线性阵列具有N个Duffing振荡器，当它们受到谐波激励时，它们由弱的线性弹簧连接。在理论分析中，可以得出以下运动方程：（1）物理坐标系，和（2）模态坐标系。运动的模态方程形成一个自参数系统，即，激励直接作用于振动的第一模式，而其他模式则被间接激励，因为它们几乎与第一模式耦合。利用Van der Pol方法求得谐波振荡的解，然后给出了频率响应曲线的表达式。在数值计算中，给出了N = 2和3时振幅和相位角的频率响应曲线。在模态坐标系中获得的频率响应曲线表明，当同时出现多个振动模式时，在物理坐标系中会发生定位现象。当N个Duffing振荡器中存在缺陷时，运动的模态方程就不会形成自参数系统，因为外部激励直接作用于所有模式。相反，在此类系统中可能会发生内部共振。

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