Conventional view holds that the damping identification method is influenced by truncation error, increasing the number of sampling points and improving the frequency resolution can reduce errors,forming a view that the more the sampling points, the smaller the damping identification error.But, the actual sampling signal usually contains noise, when the Fourier transform is applied on the sampling signal, the noise signal is also integrated together with the damping signal.It is found doing the Fourier transform on a vibration attenuation signal with the sampling time over 4.6/n(n is damping value), the amplitude of the vibration attenuation signal is inversely proportional to the number of sampling points.When using the statistical analysis on a noise signal, the actual occurrence value of the noise spectrum is not the expected value but mainly fluctuates between the expected value and the tripple of standard deviation.Through the inner product operation of the noise signal, it is shown the noise spectrum amplitude is inversely proportional to the square root of the sampling points.When the sampling time is too long, the noise signal will cover the vibration attenuation signal, which results in a larger damping identification error.Through calculations, the formula of sampling threshold was derived and verified by simulation examples and cantilever beam experiments.
Key words
sampling points /
Fourier transform /
noise /
frequency spectrum /
damping ratio
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