Elastic SH Wave Propagation in Periodic Layered Composites with a Periodic Array of Interface Cracks

Zhizhong Yan1, Chunqiu Wei1, Chuanzeng Zhang2
1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
2Department of Civil Engineering, University of Siegen, Siegen, Germany

Tóm tắt

The interaction of anti-plane elastic SH waves with a periodic array of interface cracks in a multi-layered periodic medium is analyzed in this paper. A perfect periodic structure without interface cracks is first studied and the transmission displacement coefficient is obtained based on the transfer matrix method in conjunction with the Bloch-Floquet theorem. This is then generalized to a single and periodic distribution of cracks at the center interface and the result is compared with that of perfect periodic cases without interface cracks. The dependence of the transmission displacement coefficient on the frequency of the incident wave, the influences of material combination, crack configuration and incident angle are discussed in detail. Compared with the corresponding perfect periodic structure without interface cracks, a new phenomenon is found in the periodic layered system with a single and periodic array of interface cracks.

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Tài liệu tham khảo

Hussein, M.I., Hamza, K., Hulbert, G.M. and Saitou, K., Optimal synthesis of 2D phononic crystals for broadband frequency isolation. Waves in Random and Complex Media, 2007, 17: 491–510. Cheng, Y., Xu, J.Y. and Liu, X.J., One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Physical Review B, 2008, 77: 045134. Torres, M., Montero de Espinosa, F.R. and Aragón, J.L., Ultrasonic wedges for elastic wave bending and splitting without requiring a full band gap. Phyical Review Letters, 2001, 86: 4282–4285. Kafesaki, M., Sigalas, M.M. and García, N., Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials. Physical Review Letters, 2000, 85: 4044–4047. Zhang, C.H. and Gross, D., On Wave Propagation in Elastic Solids with Cracks. Southampton, UK: Computational Mechanics Publications, 1998. Wang, Y.S., Gross, D., Interaction of harmonic waves with a periodic array of interface cracks in a multi-layered medium: anti-plane case. International Journal of Solids and Structures, 2001, 38: 4631–4655. Bostrom, A. and Golub, M., Elastic SH wave propagation in a layered anisotropic plate with interface damage modeled by spring boundary conditions. The Quarterly Journal of Mechanics & Applied Mathematics, 2009, 62(1): 39–52. Golub, Mikhail.V. and Zhang, C.Z., In-plane wave motion and resonance phenomena in periodically layered composites with a crack. Wave Motion, 2014, 51: 308–322. Golub, Mikhail.V. and Zhang, C.Z., Wang, Y.S., SH-wave propagation and resonance phenomena in a periodically layered composite with a crack. Journal of Sound and Vibration, 2011, 330: 3141–3154. Chen, A.L. and Wang, Y.S., Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals. Physica B, 2007, 392: 369–378.