Damping identification for closely spaced modes based on Bessel Inequality

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (20) : 179-184.

ZHAO Xiaodan1,HAN Junyang1,SUN Liming1,2,WANG Xifu1,

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Abstract

Closely spaced modes exist in vibration response signals widely.The damping ratio of closely spaced modes can not be identified accurately.It has been a difficult problem to improve identification accuracy of the damping ratio of closely spaced modes.A new method to estimate the damping ratio was presented.A set of basis functions were constructed nearby the closely spaced modes and processed with the Schmidt orthogonalization.The projection of vibration response signals on standard orthogonal basis functions was calculated with the inner product algorithm.The maximum of the projection was searched using a genetic algorithm and quasi-Newton methods.According to Bessel Inequality, the natural frequency and attenuation coefficient of each modal were obtained when the projection achieved the maximum value.The damping ratios could be estimated with the natural frequency and attenuation coefficient of each modal.This method is not restricted by modal density.Digital simulations and experiment show that the damping ratio of closely spaced modes can be identified accurately.This method is valuable practically.

Key words

damping ratio / closely spaced modes / bessel inequality / genetic algorithm

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ZHAO Xiaodan1,HAN Junyang1,SUN Liming1,2,WANG Xifu1,. Damping identification for closely spaced modes based on Bessel Inequality[J]. Journal of Vibration and Shock, 2018, 37(20): 179-184

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