考虑频响函数混叠误差的阻尼比识别效果研究

Study on the effect of damping ratio identification considering frequency response function aliasing error

通过实测频响函数识别阻尼比时,识别准确性受到频谱混叠现象的影响,因此建立了考虑频响函数混叠误差的阻尼比识别有效性判断方法.首先,根据傅里叶变换原理进行理论推导,证明了采样频率不足时频响函数会发生混叠现象;然后,根据频响函数混叠原理和模态叠加原理,建立了多自由度结构的基准频响混叠误差拟合公式,进而给出考虑频响函数混叠误差的阻尼比识别结果有效性判断的步骤.通过对两自由度理论频响函数模型设置不同的等效柔度比和固有频率比,表明其对两阶模态计算频响混叠误差有显著影响;通过对比四层框架结构基准模型的响应在设置不同采样频率时对阻尼比的识别结果,验证了所提方法的可行性.

When the damping ratio is identified by the measured frequency response function,the accuracy of the damping ratio identification is affected by the spectrum aliasing phenomenon.Therefore,a method for judging the effectiveness of the damping ratio identification considering the aliasing error of the frequency response function is established.Firstly,theoretical derivation is conducted according to the principle of Fourier transform,and it is demonstrated that the frequency response function will experience overlap when the sampling frequency is insufficient.Then,the fitting formula of the reference frequency response aliasing error of the multi-degree-of-freedom structure is established according to the frequency response function aliasing principle and the modal superposition principle.Subsequently,the implementation steps for judging the effectiveness of the damping ratio identification results are formed,taking into consideration the frequency response function aliasing error.By setting different equivalent flexibility ratios and natural frequency ratios for the two-degree-of-freedom theoretical frequency response function model,it is shown that they have significant influence on the frequency response aliasing error of the two-order modal calculation.By comparing the identification results of the damping ratio with the response of the four-story frame structure benchmark model at different sampling frequencies,the feasibility of the proposed method is verified.