Stressed Cylinder Dispersion Curves Based on Effective Elastic Constants and SAFE Method


Article Preview

A Semi-Analytical Finite Element (SAFE) formulation is applied to determinethe dispersion curves in homogeneous and isotropic cylindrical waveguides subject touniaxial stress. Bulk waves are required for estimating the guided wave dispersion curvesand acoustoelasticity states a stress dependence of the ultrasound bulk velocities. Therefore,acoustoelasticity influences the wave field of the guided waves. Effective Elastic Constants(EEC) has emerged as a less complex alternative to deal with the acoustoelasticity; allowinga stressed material to be assumed as an unstressed material with EEC which considers thedisturbance linked to the presence of stress. In this approach the isotropic specimen subjectto load is studied by proposing an equivalent stress-free with a modified elasticity matrixwhich terms are the EEC. EEC provides an approximate stress-strain relation facilitating thedetermination of the dispersion curves using the well-studied numerical solution for the stressfreecases reducing the complexity of the numerical implementation. Therefore, a numericalmethod combining the SAFE and EEC is presented as a tool for the dispersion curve generationin stressed cylindrical specimens. The results of this methodology are verified by comparingthem with an approach previously reported in the literature based on SAFE including the fullstrain-displacement relation



Edited by:

Luis Rodríguez-Tembleque, Jaime Domínguez and Ferri M.H. Aliabadi




J. E. Quiroga Mendez et al., "Stressed Cylinder Dispersion Curves Based on Effective Elastic Constants and SAFE Method", Key Engineering Materials, Vol. 774, pp. 295-302, 2018

Online since:

August 2018




* - Corresponding Author

[1] Alessandro Marzani, Erasmo Viola, Ivan Bartoli, Francesco Lanza di Scalea, and Piervincenzo Rizzo. A semi-analytical finite element formulation for modeling stress wave propagation in axisymmetric damped waveguides. Journal of Sound and Vibration, 318(3):488-505, (2008).


[2] Ivan Bartoli. Structural health monitoring by Ultrasonic Guided Waves. PhD thesis, University of California, San Diego, (2007).

[3] Paolo Bocchini, M Asce, Alessandro Marzani, and Erasmo Viola. Graphical User Interface for Guided Acoustic Waves. Journal of Computing in Civil Engineering, 25(June):202-210, (2011).


[4] Fabien Treyssède. Investigation of the interwire energy transfer of elastic guided waves inside prestressed cables. The Journal of the Acoustical Society of America, 140(1):498-509, (2016).


[5] A. Galvagni. Pipeline health monitoring. (September):265, (2013).

[6] P W Loveday and P D Wilcox. Guided wave propagation as a measure of axial loads in rails. Proc. SPIE, 7650:765023-765028, (2010).

[7] Philip W. Loveday. Semi-analytical finite element analysis of elastic waveguides subjected to axial loads. Ultrasonics, 49(3):298-300, (2009).


[8] P. W. Loveday, C. S. Long, and P. D. Wilcox. Semi-Analytical Finite Element Analysis of the Influence of Axial Loads on Elastic Waveguides. In D Moratal, editor, Finite Element Analysis From Biomedical Applications to Industrial Developments, chapter 18, pages 439- 454. InTech, (2012).


[9] Marc Duquennoy, Mohammadi Ouaftouh, Dany Devos, Frederic Jenot, and Mohamed Ourak. Effective elastic constants in acoustoelasticity. Applied Physics Letters, 92(24):1-3, (2008).


[10] Navneet Gandhi, Jennifer E. Michaels, and Sang Jun Lee. Acoustoelastic lamb wave propagation in a homogeneous, isotropic aluminum plate. AIP Conference Proceedings, 1335(2011):161-168, (2011).


[11] J. E. Quiroga, L. Mujica, R. Villamizar, M. Ruiz, and J. Camacho. Estimation of dispersion curves by combining Effective Elastic Constants and SAFE Method: A case study in a plate under stress. In Journal of Physics: Conference Series, volume 842, (2017).


[12] J. M. Galán and R. Abascal. Numerical simulation of Lamb wave scattering in semi-infinite plates. International Journal for Numerical Methods in Engineering, 53(5):1145-1173, (2002).


[13] H Gravenkamp. Numerical methods for the simulation of ultrasonic guided waves. PhD thesis, (2014).

[14] Hauke Gravenkamp, Chongmin Song, and Jens Prager. Numerical simulation of ultrasonic guided waves using the Scaled Boundary Finite Element Method. 0(3):2686-2689, (2012).


[15] X. Han, G. R. Liu, Z. C. Xi, and K. Y. Lam. Characteristics of waves in a functionally graded cylinder. International Journal for Numerical Methods in Engineering, 53(3):653-676, (2002).

[16] Navneet Gandhi, Jennifer E. Michaels, and Sang Jun Lee. Acoustoelastic Lamb wave propagation in biaxially stressed plates. The Journal of the Acoustical Society of America, 132(3):1284- 93, (2012).


[17] F.D. Murnaghan. Finite deformations of an elastic solid. America Journal of Mathematics, pages 235-260, (1937).

[18] S. H B Bosher and D. J. Dunstan. Effective elastic constants in nonlinear elasticity. Journal of Applied Physics, 97(10):1-7, (2005).

[19] Navneet Gandhi. Determination of dispersion curves for acoustoelastic lamb wave propagation. PhD thesis, Georgia Institute of Technology, (2010).

[20] M. Mazzotti, A. Marzani, I. Bartoli, and E. Viola. Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method. International Journal of Solids and Structures, 49(18):2359-2372, (2012).