基于解析模态分解的时变与弱非线性结构密集模态参数识别

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (19) : 1-7.

论文

基于解析模态分解的时变与弱非线性结构密集模态参数识别

王佐才，任伟新，邢云斐

作者信息 +

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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文章历史 +

摘要

对于时变与非线性的结构系统，由于结构模态响应信号的瞬时频率并不等同于结构本身的瞬时频率，因此推导了单自由度与多自由度体系在自由振动和受迫振动下模态响应信号的瞬时频率与结构本身瞬时频率的关系，理论结果表明，对于时变的线性结构和弱非线性结构，模态响应的瞬时频率缓慢变化的部分与结构系统的瞬时频率近似相等。通过对一杜芬系统的数值模拟和对一调整索力变化而使其频率变化的斜拉索自由振动实验，验证了理论结果的正确性。对于具有密集模态的时变与非线性的多自由度体系，提出了把解析模式分解方法扩展到时变与非线性结构的模态分解。该方法通过小波变换选取二分时变截止频率，对结构的时变模态响应进行分离，从而实现多自由度结构时变参数识别。最后，对一具有密集模态的两层框架时变系统受白噪声激励和地震激励进行数值模拟，结果表明，提出的方法能有效的分解时变系统的密集模态响应并能较好的识别出结构系统的瞬时频率。

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.

导出引用

王佐才;任伟新;邢云斐. 基于解析模态分解的时变与弱非线性结构密集模态参数识别[J]. 振动与冲击, 2014, 33(19): 1-7

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