Nonlinear Dynamics

, Volume 70, Issue 2, pp 1407–1420 | Cite as

Displacement modal identification method of elastic system under operational condition

  • Yunyu YinEmail author
  • Stana Živanović
  • Dongxu Li
Original Paper


Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.


Displacement modal identification Operational modal analysis (OMA) Structure dynamics 



mass, damping and stiffness matrix

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displacement, velocity and acceleration vector at time t


linear external force vector at time t


non-linear external force matrix


time, s


index of generalized displacement, j=1,2,…,j r


number of generalized displacements

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generalized displacement, velocity and acceleration vectors


jth shape function vector


shape function matrix


the jth shape function value in the position of the ith test point


jth generalized displacement value at time t k


vector of generalized displacements at time t k


index of test point, i=1,2,…,m


index of time


x coordinate of the test point along the beam’s axis


number of acceleration test points


first mode frequency, Hz


transpose of matrix


Displacement Modal Identification Method


Generalized Displacement-based Modal Identification Method




Interval of time period, s


Standard deviation


Random Decrement Technique




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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Aerospace and Materials EngineeringNational University of Defense TechnologyChangshaP.R. China
  2. 2.Science and Technology on Space Physics LaboratoryBeijingP.R. China
  3. 3.School of EngineeringWarwick UniversityCoventryUK

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