To read this content please select one of the options below:

Adaptive finite element analysis for damage detection of non-uniform Euler–Bernoulli beams with multiple cracks based on natural frequencies

Yongliang Wang (State Key Laboratory of Coal Resources and Safe Mining, School of Mechanical and Civil Engineering, China University of Mining and Technology, Beijing, China and Zienkiewicz Centre for Computational Engineering and Energy Safety Research Institute, College of Engineering, Swansea University, Swansea, UK)
Yang Ju (State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, China and State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China)
Zhuo Zhuang (Applied Mechanics Laboratory, School of Aerospace Engineering, Tsinghua University, Beijing, China)
Chenfeng Li (Zienkiewicz Centre for Computational Engineering and Energy Safety Research Institute, College of Engineering, Swansea University, Swansea, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 8 May 2018

226

Abstract

Purpose

This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems).

Design/methodology/approach

The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems.

Findings

Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.

Originality/value

The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

Keywords

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51674251, 51727807, 51608301), the State Key Research Development Program of China (Grant No. 2016YFC0600705), the National Natural Science Funds for Distinguished Young Scholars of China (Grant No. 51125017), the Fund for Creative Research and Development Group Program of Jiangsu Province (Grant No. 2014-27), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51421003), the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant No. PAPD-2014) and the China Postdoctoral Science Foundation (Grant Nos. 2015M571030, 2016M601170).

Citation

Wang, Y., Ju, Y., Zhuang, Z. and Li, C. (2018), "Adaptive finite element analysis for damage detection of non-uniform Euler–Bernoulli beams with multiple cracks based on natural frequencies", Engineering Computations, Vol. 35 No. 3, pp. 1203-1229. https://doi.org/10.1108/EC-05-2017-0176

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

Related articles