Keywords: damage location, laminated plate, modal rotation and curvature fields, shear interferometry.

The presence of damage results in perturbations or discontinuities in the modal curvature field. This fact has been extensively reported in the literature [1,2] and was recently investigated by Araújo dos Santos et al. [3], who measured mode shape displacements of a laminated composite plate using double pulsed TV holography. The numerical differentiation method proposed by Lopes et al. [4] was used to compute the second order mode shape displacement field. This method uses both differentiation and filtering techniques, in order to minimise the propagation and amplification of experimental high frequency noise. However, small perturbations in the curvature field, associated with the existence of delaminations, are in general mixed up with high frequency noise. Furthermore, these signal components, essential for damage localisation, are also attenuated or removed during the numerical differentiation procedure.

In order to overcome these problems, a new numerical-experimental method is proposed in this paper. This method is based on the computation of the curvature field from the experimental rotation field, and not, as in [3], from the experimental displacement field. The rotation fields are directly measured using a speckle shear interferometric technique. Therefore, the spatial derivative computation is reduced by one order, since the curvature field is obtained by differentiating only once the rotation field.

A carbon fibre reinforced epoxy plate is subjected to delaminations produced by two low velocity impacts. For each one of the plate states, i.e. undamaged case, impact 1 and impact 1 plus 2, the mobility function is measured and the natural frequencies identified. A shear interferometer was built for the natural mode rotation field measurements. The xx curvature fields, corresponding to the first spatial derivatives of the x axis rotation fields, are obtained by applying the numerical differentiation technique describe in [4]. These curvature fields present, for impact 1 plus 2, perturbations in several natural modes, in particular in the mode that presents the most substantial natural frequency change and the delamination area, due to impact 2, is successfully localised.

1

A.K. Pandey, M. Biswas, M.M. Samman, "Damage detection from changes in Curvature Mode Shapes", Journal of Sound and Vibration, 145(2), 321-332, 1991. doi:10.1016/0022-460X(91)90595-B

2

M.K. Yoon, D. Heider, J.W. Gillespie Jr., C.P. Ratcliffe, R.M. Crane, "Local damage detection using the two-dimensional gapped smoothing method", Journal of Sound and Vibration, 279, 119-139, 2005. doi:10.1016/j.jsv.2003.10.058

3

J.V. Araújo dos Santos, H.M.R. Lopes, M. Vaz, C.M. Mota Soares, C.A. Mota Soares, M.J.M. de Freitas, "Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography", Composite Structures, 76(3), 272-281, 2006. doi:10.1016/j.compstruct.2006.06.034

4

H.M.R. Lopes, R.M. Guedes, M.A. Vaz, "An improved mixed numerical-experimental method for stress field calculation", Optics & Laser Technology, 39(5), 1066-1073, 2007. doi:10.1016/j.optlastec.2006.04.006

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