A damage localisation method based on higher order spatial derivatives of displacement and rotation fields

This paper presents the development of a damage localisation method based on low and higher order spatial derivatives of displacement and rotation fields. The method relies on the Timoshenko beam theory, the Hamilton's principle and the Ritz method, allowing the computation of an approximate an...

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Bibliographic Details
Published in:Journal of physics. Conference series 2011-01, Vol.305 (1), p.12008-10
Main Authors: dos Santos, J V Araújo, Lopes, H M Reis, Maia, N M M
Format: Article
Language:English
Subjects:
Approximation
Beam theory (structures)
Damage
Damage localization
Derivatives
Displacement
Exact solutions
Hamilton's principle
Indicators
Localization
Localization method
Mathematical analysis
Physics
Resonant frequencies
Ritz method
Rotation
Series expansion
Thickness ratio
Timoshenko beams
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Summary:This paper presents the development of a damage localisation method based on low and higher order spatial derivatives of displacement and rotation fields. The method relies on the Timoshenko beam theory, the Hamilton's principle and the Ritz method, allowing the computation of an approximate analytical solution of natural frequencies, displacement and rotation fields. Since these fields are expressed analytically, through a series expansion, the spatial derivatives are also obtained analytically. Besides the usual curvature difference and damage index, which are based on comparisons of second order spatial derivative of the displacement field of a beam in the undamaged and damaged states, other damage indicators are proposed. These new indicators rely on spatial derivatives of rotation fields. The indicators are applied to the localisation of various cases of damages in beams and a comparison among them is carried out. It is found that, for relatively thick beams, the values of the indicators based on rotation fields spatial derivatives are, in general, lower than those based on displacement fields. It is also observed that these differences are negligible for beams with high length to thickness ratio.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/305/1/012008