A semi-analytical method for identification of thin elastic plate parameters basing on LWM

Ewa Pabisek; Zenon Waszczyszyn; Łukasz Ambroziński

Ewa Pabisek Cracow University of Technology, Poland
Zenon Waszczyszyn Rzeszow University of Technology, Poland
Łukasz Ambroziński AGH University of Science and Technology, Poland

Abstract

A new semi-analytical method, discussed in the presented paper, is composed of two stages. Stage A corresponds to the direct analysis, in which the Lamb Waves Measurements (LWM) technique enables obtaining an experimental set of points , where f and k are frequency and wavenumber, respectively. After the preprocessing in the transform space an experimental approximate curve can be formulated. In Stage B the identification procedure is simulated as a sequence of direct analyses. The dimensionless Lamb Dispersion curves are computed by means of the dimensionless simulation curve k_sim ( f | par), where the vector of plate parameters par = {E, v, d, p} is adopted, in which Young's modulus E , Poisson ratio v , plate thickness d and density p are used. The main idea of the proposed approach is similar to that in the classical method of error minimization. In our paper we propose to apply the zero error value of relative criterion Reky = 0, cf. formula (15). The formula can be applied for the identification of a single plate parameter, assuming a fixed value of the other plate parameters. This approach was used in a case study, in which Stages A and B were analysed for an aluminum plate.

Keywords

Structure Health Monitoring, non-destructive method, Lamb waves, dispersion curve, modes of vibration, elastic isotropic and homogenous plate, dentification of plate parameters,

References

[1] D. Alleyne, P. Cawley. A two-dimensional Fourier transform method for the measurement of propagating multimode signals. The Journ. Acoust. Soc. America ASA, 89: 1159–1168, 1991.
[2] Ł. Ambroziński, Ł. Paćko, T. Stepinski, T. Uhl. Ultrasonic guided waves based method for SNM: simulations and an experimental test. 5th World Conference on Structural Control and Monitoring 5WCSCM, 10443–10452, 2010.
[3] Ł. Ambroziński, P. Paćko, L. Pieczonka, T. Stepinski, T. Uhl, W.J. Staszewski. Identification of material properties – efficient modelling approach based on guided wave propagation and spatial multiple signal classification, submitted to Structural Control and Health Monitoring, 2014.
[4] V. Amirkulova. Disperspersion Relations for Elastic Waves in Plates and Rods. M.Sc. Thesis. The State Univ of New Jersey, 2011.
[5] M.M. Ettoney, S. Alampalli. Infrastructure Health Monitoring in Civil Engineering: Theory and Components. Vol. 12. CRS Press, Taylor&Francis Group, Boca Raton, London, New York, 2012.
[6] W. Ostachowicz, P. Kudela, M. Krawczyk, A. Żak. Guided Waves in Structures for SHM. J. Wiley&Sons, 2012.
[7] W. Ostachowicz, J.A. G ̋uemes (Editors). New Trends in Structural Health Monitoring. CISM Courses and Lectures vol. 542, Springer, 2013.
[8] P. Paćko, Ł. Pieczonka, Ł. Ambroziński, T. Uhl. Elastic constants identification for laminated composites based on Lamb waves. Proceedings of the 9th International workshop on Structural Health Monitoring. In: Fu-Kuo Chang [Ed.], Vol. 1, ISBN 978-1-60595-115-7, Stanford, September 10–12, 2013.
[9] E. Pabisek, Z. Waszczyszyn. Identification of thin elastic isotropic plate parameters applying ANN and GWM technique. In preparation for publication in Smart Materials and Structures.
[10] M. Sale, P. Rizo, Z. Marzani. Semi-analytical formulation for guided waves-based reconstruction of elastic moduli. Mech. Sys. Sign. Proces., 25: 2241–2256, 2011.
[11] A. Raghavan, C.E.S. Cesnik. Review of guided-wave structural health monitoring. The Shock and Vibration Digest, 39: 91–114, 2007.
[12] G.L. Rose. Ultrasonic waves in solid media. Cambridge University Press, UK, 1999.
[13] Z. Su, L. Ye. Identification of damage using Lamb waves: from fundamentals to applications. In: F. Pfeifer, P. Wriggers, ser. [Eds.], Lecture Notes in Applied and Computational Mechanics, 48, Springer, Berlin – Heidelberg, 2009.
[14] Z. Waszczyszyn, L. Ziemiański. Neural networks in the identification analysis of structural mechanics problems, In: Z. Mróz, G.E. Stavroulakis [Eds.], Parameter Identification of Materials and Structures, CISM Courses No. 469. Springer, 2005.
[15] E. Pabisek, Z. Waszczyszyn. Identification of thin elastic isotropic plate parameters applying build Wave Measurement and Artificial Neural Networks, submitted to Mechanical Systems and Signal Processing, 2014.