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Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems

机译:希尔伯特变换方法用于非线性时变振动系统的非参数辨识

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The objective of this paper is to demonstrate a Hilbert transform (HT) method for identification of mechanical time-varying vibration systems under free and forced vibration regimes. This special kind of non-stationarity arises in experimental vibration analysis and in engineering practice. The method is based on the HT of input/output signals in a time domain to extract instantaneous dynamic structure characteristics, such as natural frequencies, stiffness, damping, and their variations in time. The HT assigns a complementary imaginary part to a given real signal part, or vice versa, by shifting each component of the signal by a quarter of a period. Thus, the HT pair provides a method for determining the instantaneous amplitude and the instantaneous frequency of a signal. For general non-stationary vibration signals, the analytic signal method does a good job of simultaneous time-frequency localization of the main signal components. The paper focuses on HT signal processing techniques and identifies three groups of dynamics time-varying SDOF systems: slow varying quasi-periodic modulation of stiffness under free and forced vibration, slow varying quasi-periodic modulation of nonlinear stiffness under free vibration, and fast inter-wave parametric stiffness modulation (Mathieu equation).
机译:本文的目的是演示一种希尔伯特变换(HT)方法,用于识别自由振动和强制振动条件下的机械时变振动系统。这种特殊的非平稳性出现在实验振动分析和工程实践中。该方法基于时域中输入/输出信号的HT,以提取瞬时动态结构特征,例如固有频率,刚度,阻尼及其时间变化。 HT通过将信号的每个分量偏移四分之一周期,将补余虚部分配给给定的真实信号部分,反之亦然。因此,HT对提供了一种用于确定信号的瞬时幅度和瞬时频率的方法。对于一般的非平稳振动信号,解析信号方法在同时对主要信号分量进行时频定位方面做得很好。本文着重于HT信号处理技术,并确定了三组动态时变SDOF系统:自由振动和强迫振动下的刚度的慢速变化准周期调制,自由振动下非线性刚度的慢速变化的准周期调制以及快速振动波参数刚度调制(Mathieu方程)。

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