An application of stiffness matrix method to determining of dispersion curves for arbitrary composite materials

• Autorzy: Barski M. , Pająk P.

Identyfikatory

DOI

10.5604/12314005.1213520

• Języki publikacji: EN

Abstrakty

EN

Nowadays multi-layered composite material is very often applied in different kind of structures, like aircrafts, boats or vehicles. Parts of structures, which are made of these materials, are significantly lighter in comparison with traditional materials, like aluminum or steel alloys. On the other hand, the process of damage creation and evolution in the case of composites is much more complex. Moreover, the damages, which are characteristic for multi-layered materials (matrix cracking, fibre breakage, delaminations), are very difficult to detect at early stage of creation. Hence, there is a need to develop the advanced methods to detect them without destroying tested composite element. One of them is based on analysis of elastic wave propagation through the composite structure. Unfortunately, elastic waves possess strongly dispersive character. Thus, it is necessary to determine dispersion curves for investigated material before the tests in order to appropriate interpretation of received dynamic response of structure. In the case of arbitrary composite materials, it is rather challenging task. In the present article the relatively new, analytical method is applied, namely stiffness matrix method. The fundamental assumptions and the theoretical formulation of this method are discussed. Next numerical examples are presented, namely the dispersion curves are determined for the single orthotropic lamina and multi-layered 'quasi - isotropic' composite plate. The studied plates are made of glass fibres and epoxy resin. In the case of single lamina, the dispersion curves are determined in the parallel, perpendicular and arbitrary direction of waves propagation with respect to the fibre direction. In the case of multi-layered plates, the dispersion curves are computed for one arbitrary direction. Additionally, the phase and group velocities for fundamental modes and fixed excitation frequency are estimated in all directions of waves propagation.

Słowa kluczowe

EN

SHM system; multi-layered composites; elastic waves; dispersion curves; stiffness matrix method

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2016
• Tom: Vol. 23, No. 1
• Strony: 47--54
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Barski M.

• Cracow University of Technology, Department of Mechanical Engineering Jana Pawła II Avenue 37, 31 - 864 Krakow, Poland tel.: [phone], fax: [phone]

autor

Pająk P.

• Cracow University of Technology, Department of Mechanical Engineering Jana Pawła II Avenue 37, 31 - 864 Krakow, Poland tel.: [phone], fax: [phone]

Bibliografia

• [1] Giurgiutiu, V., Structural Health Monitoring with Piezoelectric Wafer Active Sensors, Elsevier, 2008.
• [2] Haskell, N. A., Dispersion of surface waves on multi-layered media, Bulletin of Seismological Society of America, Vol. 43, pp. 17-34, 1953.
• [3] Hawwa, M. A., Nayfeh, H. A., The general problem of thermoelastic waves in anisotropic periodically laminated composites, Composites Engineering, Vol. 5(12), pp. 1499-1517, 1991.
• [4] Kamal, A., Giurgiutiu, V., Stiffness Transfer Matrix Method (STMM) for Stable Dispersion Curves Solution in Anisotropic Composites, Proceedings of SPIE, Vol. 9064, 2014.
• [5] Kausel, E., Wave propagation in anisotropic media, International Journal for Numerical Methods in Engineering, Vol. 23, pp. 1567-1578, 1986.
• [6] Knopoff, L., A matrix method for elastic waves problems, Bulletin of Seismological Society of America, Vol. 43, pp. 431-438, 1964.
• [7] Lowe, J. S., Matrix Techniques for Modeling Ultrasonic Waves in Multilayered Media, IEEE Transactions on Ultrasonics, Ferroelectric and frequency Control, Vol. 42(2), pp. 525-542, 1995.
• [8] Muc, A., Mechanics of fibre composites (in Polish), Księgarnia Akademicka, Krakow, 2003.
• [9] Nayfeh, A. H., The general problem of elastic wave propagation in multi-layered anisotropic media, Journal of Acoustic Society of America, Vol. 89(4), pp. 1521-1531, 1991
• [10] Pant, S., Laliberte, J., Martinez, M., Rocha, B., Derivation and experimental validation of Lamb wave equations for an n - layered anisotropic composite laminate, Composite Structure, Vol. 111, pp. 566-579, 2014.
• [11] Rokhlin, S. I., Wang, L., Stable recursive algorithm for elastic wave propagation in layered anisotropic media: Stiffness matrix method, Journal of Acoustic Society of America, Vol. 112, pp. 822-834, 2002.
• [12] Rokhlin, S. I., Wang, L., Ultrasonic wave in layered anisotropic media: characterization of multidirectional composites, International Journal of Solids & Structures, Vol. 39, pp. 5529-5545, 2002.
• [13] Thompson, W. T., Transmission of elastic waves through a stratified solid medium, Journal of Applied Physics, Vol. 21, pp. 89-93, 1950.
• [14] Wang, L., Rokhlin, S. I., Stable reformulation of transfer matrix method in layered anisotropic media, Ultrasonics, Vol. 39, pp. 413-424, 2001.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.