Keywords: low mass impact, dynamic analysis, wave propagation, experimental measurements.

This work presents a numerical and experimental study for small mass impact in an aluminium plate. The transient response in a plate subjected to a low velocity impact is governed by bend wave propagation. For successive time instants the out-of-plane displacements due to the bending waves were assessed using double pulse ESPI technique. The impact force was measured and recorded with a force transducer. The explicit ABAQUSmodule was used to numerically simulate the transient response of the plate. The measured experimental impact force was used as input for the numerical simulation. Comparisons between numerical and experimental displacement results are presented.

Holographic interferometry names a metrology technique, based on the correlation between two or more wave fronts being, at least, one of them reconstructed from a hologram. The interferogram results from the correlation between wave fronts and corresponds to a set of fringes indicating points undergoing equal displacement / amplitude of vibration. The correlation between wave fronts can be performed by one of the following ways: real time, time-average and double exposure. Only the last two can be applied when dynamic phenomena are investigated. In a time-average recording several cycles of vibration are added in the same interferogram so the object should be undergoing a steady harmonic vibration. Finally, the double exposure correlation can be used to study quick dynamic phenomena like vibrations and transient displacements.

Double exposure correlation can be performed at any time after the recording of two or more holograms. However, the time between recordings should be carefully selected to avoid displacements out of the measuring range of the technique. After wave fronts correlation a fringe pattern, overlaying the object, is generated. These fringes represent points of equal displacement in the direction of the sensitivity vector [1].

When holographic interferometry is associated to image-processing techniques the enormous quantity of data available in each measurement can be easily processed and interpreted [2]. Several image-processing algorithms are already available to help in the result presentation.

In this study, high repeatability of the experimental analysis was achieved allowing recordings with different time delays that can be used for a postponed reconstruction of the wave propagation. As expected, the waves are circular and concentric due to the isotropic properties of the aluminium. As the temporal evolution of the impact load is of primordial importance in the numerical simulation of the wave propagation, it was always recorded.

The propagation of bending waves in isotropic plates was simulated using the explicit module of the ABAQUScode. For this propose the object was discretised into a 2800 shell elements mesh. In all the calculations performed was used the four nodes element (S4R) without damping.

From the results obtained in this work with an isotropic plate the selected methodology proved to be well adapted to the objectives of the research program. The measures already performed allowed the set-up adjustments. A set of numerical procedures were implemented allowing a complete recording of the experimental data and its preprocessing to be used as input in a FEM code.

The calculations already done with ABAQUScode can be considered a quite good approximation to the wave propagation. This prompts high expectations for the development of a numerical model to precisely simulate dynamic behavior of plates. Future developments will be implemented to extend the application of this methodology to anisotropic materials. Experimental techniques are used to access the displacement field, being the stress calculation based on that information. If the material properties are known, this last step can be achieved by two different ways. Either using an hybrid experimental-numerical technique or by direct differentiation of the measured displacements field. A major challenge will be to solve the problem inversely by using the experimental data to extract the material properties.

Acknowledgments

This work was partially funded by Fundação para a Ciência e Tecnologia - FCT under the project POCTI/EME/40048/2001. Jaime Monteiro, Fernando Ferreira and Jorge Reis are acknowledged by its collaboration in the implementation of the experimental set-up.

1

Burch, J. M.; Holographic Measurement of Displacement and Strain, Journal of Strain Analysis 9(1), 1-3, 1974. doi:10.1243/03093247V091001

2

Chousal, J.A.G.; Processamento de Imagem na Interpretação de Franjas Interferométricas em Análise Experimental de Tensões, (Image processing in the interpretation of interferometric fringes in Experimental Mechanics), MSc Thesis, FEUP, 1991.

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