Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach |
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Authors: | MA Zhisai LIU Li ZHOU Sida NAETS Frank HEYLEN Ward DESMET Wim |
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Affiliation: | 1.School of Aerospace Engineering, Beijing Institute of Technology, 100081, Beijing, China ;2.Department of Mechanical Engineering, KU Leuven, 3001, Leuven, Belgium ; |
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Abstract: | The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the “frozen-time” assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stability-preserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system’s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam experimental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes. |
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