Keywords: elastic guided waves, wave finite element, dispersion relationship, structural health monitoring.

Recently, many studies focus on the analysis of elastic guided waves and their practical applications in structural health monitoring (SHM) for large scale structures [1,2]. These structures can be regarded as assemblies of periodic components, including uniform waveguide structures or generally periodic systems comprised of an arbitrary substructure. In this study, we propose a convenient and efficient numerical approach for the investigation of the health monitoring of these structures. A wave finite element (WFE) formulation is used [3,4]. The dispersion relationship and wave modes are extracted based on the post-processing of the system matrices from the commercial finite element (FE) packages. They are formulated to calculate the frequency response of both the intact and locally flawed structures. In the case that the typical components have a large number of degree of freedoms, they are condensed by using component mode synthesis before the construction of the eigenfunction.

Using the proposed wave representation method, the higher frequency response of those waveguide structures can be conveniently examined. The connection with the standard FE method enables dynamic problems of the waveguide containing local damage to be studied with ease. The time response can be calculated by either the frequency response function or the wave propagation approach. The wide band solution allows the transient response of the intact or damaged waveguide structure to be examined. The response of waveguides with various type of defects and subjected to different incident waves can be fully studied. This will provide some important information for the practical investigation using the elastic guide waves for damage detection. The proposed numerical method can also be extended to the analysis of more complex structures such as multiple or interconnected waveguides.

1

J.L. Rose, M.J. Avioli, P. Mudge et al., "Guided wave inspection potential of defects in rail", NDT&E International, 37, 153-161, 2004. doi:10.1016/j.ndteint.2003.04.001

2

J.L. Rose, "Ultrasonic guided waves in structural health monitoring", Key Engineering Materials, 270-273, 14-21, 2004. doi:10.4028/www.scientific.net/KEM.270-273.14

3

L. Houillon, M. Ichchou, L. Jezequel, "Dispersion curves of fluid filled elastic pipes by standard fe models and eigenpath analysis", Journal of Sound and Vibration, vol. 281, pp. 483-507, 2005.

4

M. Maess, N. Wagner, L. Gaul, "Dispersion curves of fluid filled elastic pipes by standard fe models and eigenpath analysis", Journal of Sound and Vibration, vol. 296, pp. 264-276, 2006. doi:10.1016/j.jsv.2006.03.005

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