标题： 基于锁相环测试的非线性系统二次谐振识别 显示英文标题

标题： Identification of Secondary Resonances of Nonlinear Systems using Phase-Locked Loop Testing

摘要： 非线性动力学系统的一个独特特征是在主要共振之外还存在次谐共振和超谐共振。在这项研究中，介绍了一种有效的振动测试方法，用于实验识别这些二次共振。所提出的方法依赖于基于锁相环控制与自适应滤波器相结合的在线傅里叶分解。为此，利用共振相位滞后概念来定义在实验连续过程中需要跟踪的目标相位滞后。该方法通过两个具有三次非线性的系统进行演示，即数值杜芬振子和由夹紧-夹紧薄梁组成的物理实验。获得的结果表明，该控制方案可以准确表征二次共振并追踪它们的主曲线。所开发算法的一个特别显著特征是，从静止位置开始，它能够实现向次谐孤立分支某一点的自动平滑动态状态转移，从而诱导分支切换。 显示英文摘要

摘要： One unique feature of nonlinear dynamical systems is the existence of superharmonic and subharmonic resonances in addition to primary resonances. In this study, an effective vibration testing methodology is introduced for the experimental identification of these secondary resonances. The proposed method relies on phase-locked loop control combined with adaptive filters for online Fourier decomposition. To this end, the concept of a resonant phase lag is exploited to define the target phase lag to be followed during the experimental continuation process. The method is demonstrated using two systems featuring cubic nonlinearities, namely a numerical Duffing oscillator and a physical experiment comprising a clamped-clamped thin beam. The obtained results highlight that the control scheme can accurately characterize secondary resonances as well as track their backbone curves. A particularly salient feature of the developed algorithm is that, starting from the rest position, it facilitates an automatic and smooth dynamic state transfer toward one point of a subharmonic isolated branch, hence, inducing branch switching.