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首页> 外文期刊>Applied Mathematical Modelling >1∶2 and 1∶3 internal resonance active absorber for non-linear vibrating system
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1∶2 and 1∶3 internal resonance active absorber for non-linear vibrating system

机译：用于非线性振动系统的1∶2和1∶3内部共振有源吸收器

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摘要

Vibration and dynamic chaos should be controlled in either structures or machines. An active vibration absorber for suppressing the vibration of the non-linear plant when subjected to external and parametric excitations is studied in the presence of one-to-two and one-to-three internal resonance. The main attention is focused on the study of the active control and stability of two systems, which can be used to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to determine four first-order non-linear ordinary differential equations that govern the modulation of the amplitudes and phases in the presence of internal resonance of the two systems with quadratic and cubic order of control. These equations are used to determine the steady state solutions and their stability. The stability study of non-linear periodic solution for two cases (1:2 and 1:3 internal resonance) and the stability of the obtained numerical solution are investigated using frequency, force-response curves and phase-plane method. Also, effects of some parameters on the steady state solution of the vibrating system are investigated and reported in this paper. Variation of some parameters leads to the bending of the frequency, force-response curves and hence to the jump phenomenon occurrence. The reported results are Compared to the available published work.
机译：在结构或机器中都应控制振动和动态混乱。在存在一对一和一对三的内部共振的情况下，研究了一种用于抑制非线性设备在受到外部和参数激励时的振动的主动减振器。主要注意力集中在两个系统的主动控制和稳定性研究上，这两个系统可用于减少由于转子叶片拍打运动而引起的振动。应用多尺度摄动技术的方法来确定四个一阶非线性常微分方程，这些方程在两个系统具有二次和三次阶的内部共振的情况下，控制振幅和相位的调制。这些方程式用于确定稳态解及其稳定性。使用频率，力响应曲线和相平面法研究了两种情况（1：2和1：3内部共振）的非线性周期解的稳定性以及所得数值解的稳定性。此外，本文还研究了一些参数对振动系统稳态解的影响。一些参数的变化会导致频率，力响应曲线的弯曲，从而导致出现跳变现象。将报告的结果与可用的已发表工作进行比较。

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