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Flexibility-based structural damage identification using Gauss–Newton method

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Abstract

Structural damage will change the dynamic characteristics, including natural frequencies, modal shapes, damping ratios and modal flexibility matrix of the structure. Modal flexibility matrix is a function of natural frequencies and mode shapes and can be used for structural damage detection and health monitoring. In this paper, experimental modal flexibility matrix is obtained from the first few lower measured natural frequencies and incomplete modal shapes. The optimization problem is then constructed by minimizing Frobenius norm of the change of flexibility matrix. Gauss–Newton method is used to solve the optimization problem, where the sensitivity of flexibility matrix with respect to structural parameters is calculated iteratively by only using the first few lower modes. The optimal solution corresponds to structural parameters which can be used to identify damage sites and extent. Numerical results show that flexibility-based method can be successfully applied to identify the damage elements and is robust to measurement noise.

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Acknowledgments

The authors thank the support of the Texas Institute for the Intelligent Bio-Nano Materials and Structure for Aerospace Vehicles, funded by NASA Cooperative Agreement no. NCC-1-02038.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Rice University, Houston, TX, 77005, USA

    B CHEN & S NAGARAJAIAH

  2. Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX, 77005, USA

    S NAGARAJAIAH

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  1. B CHEN
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  2. S NAGARAJAIAH
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Correspondence to S NAGARAJAIAH.

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CHEN, B., NAGARAJAIAH, S. Flexibility-based structural damage identification using Gauss–Newton method. Sadhana 38, 557–569 (2013). https://doi.org/10.1007/s12046-013-0151-3

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  • DOI: https://doi.org/10.1007/s12046-013-0151-3

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