Analytical Mode Decomposition Based Time-Varying and Weakly Nonlinear Structural Identification with Closely-Spaced Modes

Wang Zuo-cai;Ren Wei-xin;and Xing Yun-fei

Journal of Vibration and Shock ›› 2014, Vol. 33 ›› Issue (19) : 1-7.

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PDF(2309 KB)
Journal of Vibration and Shock ›› 2014, Vol. 33 ›› Issue (19) : 1-7.
论文

Analytical Mode Decomposition Based Time-Varying and Weakly Nonlinear Structural Identification with Closely-Spaced Modes

  • Wang Zuo-cai, Ren Wei-xin, and Xing Yun-fei
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Abstract

The instantaneous frequency of modal response is not equal to the instantaneous frequency of the structural system for a time-varying and nonlinear structure. In this paper, the structural instantaneous frequencies are directly derived from the decomposed modal responses for single- and multiple- degree-of-freedom systems with both free and force vibrations. The theoretical result shows that the slow-varying component of the signal’s instantaneous frequency is approximately equal to the systems instantaneous frequency for slowly time-varying linear structures and weakly nonlinear structures. The result is validated by a numerical simulation of a Duffing system and an experimental test of a cable with time-varying tension force and frequency. For a time-varying and nonlinear structure with closely-spaced modes, this paper extended analytical mode decomposition into time signals with time-varying frequencies. The mathematical foundation for this new extension is provided and an approach with wavelet transform is developed for the selection of time-varying bisecting frequencies. Finally, a two-story time-varying structure with closely-spaced modes subjected both white noise and earthquake excitations are analyzed, the result show that proposed method can effectively decomposed modal responses and accurately estimated the instantaneous frequency of time-varying and nonlinear structures.

Key words

Analytical mode decomposition / instantaneous frequency / Modal parameter identification / time-varying and nonlinear structure

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Wang Zuo-cai;Ren Wei-xin;and Xing Yun-fei. Analytical Mode Decomposition Based Time-Varying and Weakly Nonlinear Structural Identification with Closely-Spaced Modes[J]. Journal of Vibration and Shock, 2014, 33(19): 1-7
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