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research-article

Extended smooth orthogonal decomposition for modal analysis

[+] Author and Article Information
Zhixiang Hu

Department of Civil Engineering, Hefei University of Technology, Hefei, Anhui Province 23009, China
huzhixiang@hfut.edu.cn

Xiao Huang

The 38th Research Institute of CETC, Hefei, Anhui Province 230088, China
huangxcetc@163.com

Yixian Wang

Department of Civil Engineering, Hefei University of Technology, Hefei, Anhui Province 23009, China
wangyixian2012@hfut.edu.cn

Feiyu Wang

Department of Civil Engineering, Hefei University of Technology, Hefei, Anhui Province 23009, China
wfy919200@163.com

1Corresponding author.

ASME doi:10.1115/1.4039240 History: Received September 25, 2017; Revised January 05, 2018

Abstract

The smooth orthogonal decomposition (SOD) is an output-only modal analysis method which has simple structure and gives good results for un-damped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate varies measurements that contain the displacement, the velocity, the acceleration and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the un-damped vibration system. These different methods are called ESOD methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different with each other. Thus a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the SDOF vibration systems, it is effective for the MDOF vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for un-damped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.

Copyright (c) 2018 by ASME
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