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Title: Vibration source identification using an energy density method
Authors: Mao, C 
Wong, WO 
Cheng, L 
Issue Date: Dec-2022
Source: Journal of vibration and control, Dec. 2022, v. 28, no. 23-24, p. 3859-3874
Abstract: The localization of shaking forces acting on an operating machine is an important step to identify vibration and noise sources. The forced vibration response of a linearly vibrating structure is assumed to be linear. However, the energy distribution of a linearly vibrating structure contains “coupled terms” in the modal decomposition of the vibration energy density function. These coupled energy terms represent the cross-modal energy density associated with the exciting force of a dynamic structure under forced vibration. In this research, it is proved analytically that the high-order cross-modal energy densities of a linear dynamic structure are highly correlated to the location of the external exciting force. Using this finding, a new force localization index based on the high-order cross-modal energy densities of a dynamic structure is proposed and tested. Numerical tests on uniform and step beam structures under force excitation with different frequencies and locations have been carried out to test the effectiveness of the proposed force localization method. It is found that the proposed force localization method works well on vibrating beam structures. Experiments are carried out to verify the proposed force localization method.
Keywords: Vibration source identification
Force localization
Energy density
Vibration energy
Publisher: SAGE Publications
Journal: Journal of vibration and control 
ISSN: 1077-5463
EISSN: 1741-2986
DOI: 10.1177/10775463211039903
Rights: This is the accepted version of the publication Mao C, Wong WO, Cheng L. Vibration source identification using an energy density method. Journal of Vibration and Control. 2022;28(23-24):3859-3874. doi:10.1177/10775463211039903. Copyright © 2021 (The Author(s)). DOI:10.1177/10775463211039903.
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