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Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

机译:用零早期快速傅立叶变换估算瞬态响应中的非线性程度

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This work presents time-frequency signal processing methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed zeroed early-time fast Fourier transforms (ZEFFTs), acquire the usual shape of linear frequency response functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip and impact nonlinearities.
机译:这项工作提出了时频信号处理方法,用于检测和表征瞬态响应测量中的非线性。该方法适用于其响应随着幅度衰减而变得越来越线性的系统。在初始响应的各个部分都设置为零的情况下,可以找到响应数据的离散傅立叶变换。这些频率响应被称为零早期快速傅立叶变换(ZEFFT),随着更多的初始非线性响应被消除,获得了线性频率响应函数(FRF)的通常形状。因此,随着初始无效部分的长度变化,ZEFFT形状的质变证明了非线性。这些光谱显示出对非线性敏感,揭示了它的存在,即使它仅在响应的前几个周期中是活动的,例如机械接头中的大滑移。他们还提供了对非线性特性的洞察力,有可能揭示出模态之间或模态幅度之间的非线性能量转移,在该能量或模态幅度以下,系统会线性运行。在某些情况下,可以从较晚的时间确定线性模型,即线性响应,并使用它来重构系统在线性的情况下在先前时间执行的响应。这表明了非线性的严重性及其对测量响应的影响。该方法在来自具​​有滑移和冲击非线性的系统的分析和实验数据上均得到了证明。

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