Wave Propagation Modelling in Composite Plates


Article Preview

The paper presents results of numerical simulation for transverse elastic waves corresponding to A0 mode of Lamb waves propagating in a composite plate. This problem is solved by using the Spectral Finite Element Method. Spectral plate elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of selecting Lagrange polynomials discrete orthogonality guaranteed leading to a diagonal mass matrix. This results in a crucial reduction of numerical operations required for a chosen time integration scheme. Numerical calculations have been carried out for various orientations of reinforcing fibres within the plate as well as for various fibre volumes fractions. The paper shows that the velocities of transverse elastic waves in composite materials are functions of the fibre orientation and the fibre volume fraction.



Edited by:

Tadeusz Uhl and Andrzej Chudzikiewicz




P. Kudela and W. M. Ostachowicz, "Wave Propagation Modelling in Composite Plates ", Applied Mechanics and Materials, Vol. 9, pp. 89-104, 2008

Online since:

October 2007




[1] J.R. Vinson and R.L. Sierakowski: Behavior of structures composed of composite materials. (Martinus-Nijhoff, Inc., 1989).

[2] O.O. Ochoa and J.N. Reddy: Finite element analysis of composite laminates (Kluwer Academic Publishers, 1992).

[3] J.M. Whitney: Structural analysis of laminated anisotropic plates (Technomic Publishing Co., 1987).

[4] A.L. Kalamkarov: Composite and reinforced elements of construction (John Wiley & Sons Inc., 1992).

[5] R.M. Jones: Mechanics of Composite Materials (Taylor & Francis Inc., 1999).

[6] M. Krawczuk, W.M. Ostachowicz and A. Żak: Computational Mechanics Vol. 20 (1997), pp.79-83.

[7] L.J. Bond, in: Elastic waves and ultrasonic non-destructive evaluation, edited by S.K. Datta, J. D Achenbach and Y.S. Rajapakse, North-Holland, Amsterdam (1990).

[8] J.C. Strickwerda: Finite difference schemes and partial differential equations (WadsworthBrooks, Belmont, 1989).

[9] H. Yamawaki and T. Saito: NDT&E International Vol. 8-9 (1992), pp.379-389.

[10] O.C. Zienkiewicz: The finite element method (McGraw-Hill, 1989).

[11] R.J. Talbot and J.S. Przemieniecki: International Journal of Solids and Structures Vol. 11 (1976), pp.115-138.

[12] M. Koshiba, S. Karakida. and M. Suzuki: IEEE Transactions on Sonic and Ultrasonic Vol. 31 (1984), pp.18-25.

[13] G.S. Verdict, P.H. Gien and C.P. Burger, in: Review of Progress in Quantitative Nondestructive Evaluation, edited by D.O. Thompson and D.E. Chimenti Vol. 11 (1992), pp.97-104.

[14] D.N. Alleyne and P. Cawley: NDT&E International Vol. 25 (1992), pp.11-22.

[15] C.A. Brebbia, J.C.F. Tells and L.C. Wrobel: Boundary elements techniques (Springer, Berlin, 1984).

[16] Y. Cho and J.L. Rose: Journal of the Acoustical Society of America Vol. 99 (1996), pp.2079-2109.

[17] Y.K. Cheung: Finite strip method in structural analysis (Pergamon Press, 1976).

[18] G.R. Liu and Z.C. Xi: Elastic waves in anisotropic laminates (CRC Press, 2002).

[19] G.R. Liu, J. Tani, K. Watanabe and T. Ohyoshi: Journal of Sound and Vibration Vol. 139 (1990), pp.313-330.

[20] T. Liu, K. Liu and J. Zhang: Computer Methods in Applied Mechanics and Engineering Vol. 193 (2004), pp.2427-2452.

[21] T. Liu, K. Liu and J. Zhang: Archive of Applied Mechanics Vol. 74 (2005), pp.477-488.

[22] PP. Delsanto and R.B. Mignogna: Journal of Acoustical Society of America Vol. 104 (1998) pp.1-8.

[23] H. Yim and Y. Sohn: IEEE Transactions on Ultrasonic, Ferroelectrics, and Frequency Control Vol. 47 (2000), pp.549-558.

[24] P.P. Delsanto, T. Whitecomb, H.H. Chaskelis and R.B. Mignogna: Wave Motion Vol. 16 (1992), pp.65-80.

[25] P.P. Delsanto, T. Whitecomb, H.H. Chaskelis, R.B. Mignogna and R.B. Kline: Wave Motion Vol. 20 (1994), pp.295-314.

DOI: 10.1016/0165-2125(94)90016-7

[26] P.P. Delsanto, R.S. Schechter and R.B. Mignogna: Wave Motion Vol. 26 (1997), pp.329-339.

[27] J.F. Doyle: Wave propagation in structures (Springer-Verlag, 1997).

[28] A.T. Patera: Journal of Computational Physics Vol. 54 (1984), pp.468-488.

[29] M. Krawczuk , M. Palacz and W. Ostachowicz: Journal of Sound and Vibration Vol. 264 (2003), pp.1139-1153.

[30] D.R. Mahapatra and S. Golpalakrishnan: Computers and Structures Vol. 59 (2003) pp.67-88.

[31] M. Palacz, M. Krawczuk: Computers and Structures Vol. 80 (2002), pp.1809-1816.

[32] S.A. Rizzi and J.F. Doyle: Journal of Vibration and Acoustics Vol. 114 (1992), pp.569-577.

[33] J.P. Boyd: Chebyshev and Fourier spectral methods (Springer, 1989).

[34] C. Pozrikidis: Introduction to Finite and Spectral Element Methods using MATLAB® (Chapman & Hall/CRC, 2005).

[35] C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang: Spectral methods in fluid dynamics (Springer, 1988).

DOI: 10.1007/978-3-642-84108-8_1

[36] R. Spall: International Journal of Heat Mass Transfer Vol. 15 (1995), pp.2743-2748.

[37] W. Dauksher and A.F. Emery, in: Review of Progress in Quantitative Non-destructive Evaluation, edited by D.O. Thompson and D.E. Chimenti Vol. 15 (1996), pp.97-104.

[38] G. Seriani: Computational Methods Applied in Mechanical Engineering Vol. 164 (1998), pp.235-247.

[39] http: /mathworld. wolfram. com.

[40] M. Kleiber: Incremental finite element modelling in non-linear solid Mechanics (J. Wiley & Sons, New York, 1989).

Fetching data from Crossref.
This may take some time to load.