Modal Analysis for Localization of Harmonic Oscillations in Nonlinear Oscillator Arrays
Modal Analysis for Localization of Harmonic Oscillations in Nonlinear Oscillator Arrays
复制标题
非线性振荡器阵列中谐波振荡本地化的模态分析
DOI：
10.1115/1.4055430
复制
发表时间：
2022
影响因子：
2
通讯作者：
Ikeda Takashi
中科院分区：
文献类型：
--
作者：
Harata Yuji;Ikeda Takashi
当非线性振荡器阵列被谐波激励时，阵列中的特定振荡器可以以大幅度振荡。这就是所谓的本地化现象，然而，本地化的原因至今尚未澄清。因此，本研究的目的是阐明在非线性振子阵列的本地化的原因。从理论上研究了由N个线性弹簧连接的Duffing振子在外力和简谐力作用下的非线性振子阵列的行为。将物理坐标系下的运动方程转化为模态运动方程，揭示了当阵列由相同振子组成时，在模态坐标系下构成一个自参数系统。第一阶振动模态是由外力直接激励的，而其余的模态则是由与第一阶模态耦合的非线性项间接激励的。利用货车der Pol方法得到了系统的近似解。给出了N = 2和3时物理坐标和模态坐标下的频率响应曲线。当多个模式同时被激发时，可以发生局部化。此外，恢复力的缺陷上的双Duffing振子阵列的响应的影响进行了检查。
When a nonlinear oscillator array is harmonically excited, specific oscillators in the array may oscillate with large amplitudes. This is known as the localization phenomenon; however, the reason for localization has not been clarified thus far. Thus, the aim of this study is to elucidate the reason for localization in nonlinear oscillator arrays. We theoretically investigated the behavior of a nonlinear oscillator array, which consists of N Duffing oscillators connected by linear springs under external and harmonic forces. The equations of motion in physical coordinates are transformed into modal equations of motion, which reveal that the array forms an autoparametric system in the modal coordinates when it consists of identical oscillators. The first mode of vibration is directly excited by the external force, whereas the remaining modes are indirectly excited by the nonlinear terms coupled with the first mode. The approximate solutions of the harmonic oscillations were obtained using van der Pol's method. The frequency response curves (FRCs) for both the physical and modal coordinates for N = 2 and 3 are presented. Localization can occur when multiple modes are excited simultaneously. Furthermore, the effects of imperfections in the restoring forces on the responses of the two-Duffing-oscillator array are examined.