Abstract
Vibration based methods are commonly deployed to detect structural damage using sensors placed remotely from potential damage sites. Whilst many such techniques are modal based there are advantages to adopting a wave approach, in which case it is essential to characterise wave propagation in the structure. The Wave Finite Element method (WFE) is an efficient approach to predicting the response of a composite waveguide using a conventional FE model of a just a short segment. The method has previously been applied to different structures such as laminated plates, thinwalled structures and fluid-filled pipes. In this paper, the WFE method is applied to a steel reinforced concrete beam. Dispersion curves and wave mode shapes are first presented from free wave solutions, and these are found to be insensitive to loss of thickness in a single reinforcing bar. A reinforced beam with localised damage is then considered by coupling an FE model of a short damaged segment into the WFE model of the undamaged beam. The fundamental bending, torsion and axial waves are unaffected by the damage but some higher order waves of the cross section are significantly reflected close to their cut-on frequencies. The potential of this approach for detecting corrosion and delamination in reinforced concrete beams will be investigated in future work.
Highlights
Most damage in reinforced concrete structures comprising steel bars is due to corrosion and delamination
The Wave Finite Element method (WFE) method is applied to a steel reinforced concrete beam
Dispersion curves and wave mode shapes are first presented from free wave solutions, and these are found to be insensitive to loss of thickness in a single reinforcing bar
Summary
Most damage in reinforced concrete structures comprising steel bars is due to corrosion and delamination. 2. WFE formulation The WFE concept relies on the notion of predicting the wave characteristics of a structure through analysing the wave propagation within a short section of the waveguide, and by expressing the continuity of displacements and equilibrium of forces at the boundaries between successive segments, an eigenvalue problem is posed in terms of a transfer function across the section. WFE formulation The WFE concept relies on the notion of predicting the wave characteristics of a structure through analysing the wave propagation within a short section of the waveguide, and by expressing the continuity of displacements and equilibrium of forces at the boundaries between successive segments, an eigenvalue problem is posed in terms of a transfer function across the section By solving this problem at each specified frequency, the eigenvalues obtained,that are related to the wavenumbers of the waveguide, relate the variables to the right and left side of the section, and the eigenvectors are associated with the displacement and forces at this section.
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