Abstract
In the present chapter we consider both computer and natural experimental approaches for the wave propagation through an elastic material with the doubly-periodic system of holes. The numerical study is performed by applying the Boundary Integral Equation method with further discretization to the algebraic system by the Boundary Element Method. A wide range of numerical experiments is conducted for different setups of the doubly periodic system, varying distances, sizes of the holes and their locations. The influence of hole cross-sections on the wave-transmission coefficient is examined by considering different star-like shapes. Natural experiments are based on the ultrasonic testing performed for the steel and plastic materials with the system of small holes. The experimental data are analyzed from the point of their spectral characteristics as well as the amplitude-time dependence.
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References
Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover, New York (1965)
Achenbach, J.D., Li, Z.L.: Reflection and transmission of scalar waves by a periodic array of screens. Wave Motion 8, 225–234 (1986)
Achenbach, J.D., Kitahara, M.: Harmonic waves in a solid with a periodic distribution of spherical cavities. J. Acoust. Soc. Am. 81, 595–598 (1987)
Banerjee, P.K.: The Boundary Element Methods in Engineering, 2nd edn. McGraw-Hill, London (1994)
Banerjee, B.: An Introduction to Metamaterials and Waves in Composites. CRC Press, Boca Raton (2011)
Bron, S.: Efficient numerical methods for non-local operators. EMS Tracts Math. 14 (2010)
Brunner, D., Junge, M., Rapp, P., Bebendorf, M., Gaul, L.: Comparison of the fast multipole method with hierarchical matrices for the helmholtz-BEM. Comput. Model. Eng. Sci. 58, 131–158 (2010)
Cheng, H., Crutchfield, W.Y., Gimbutas, Z., et al.: A wideband fast multipole method for the Helmholtz equation in three dimensions. J. Comput. Phys. 216, 300–325 (2006)
Deymier, P.A.: Acoustic Metamaterials and Phononic Crystals. Springer, Berlin (2013)
Guenneau, S., Craster, R.V.: Acoustic Metamaterials Negative Refraction, Imaging, Lensing and Cloaking. Springer, Netherlands (2013)
Liu, Z., Zhang, X., Mao, Y., et al.: Locally resonant sonic materials. Science 289, 1734–1736 (2000)
Cho, M.H., Cai, W.: A wideband fast multipole method for the two-dimensional complex Helmholtz equation. Comput. Phys. Commun. 181, 2086 (2010)
Scarpetta, E., Sumbatyan, M.A.: On wave propagation in elastic solids with a doubly periodic array of cracks. Wave Motion 25, 61–72 (1997)
Scarpetta, E., Sumbatyan, M.A.: Wave propagation through a periodic array of inclined cracks. Eur. J. Mech. A/Solids. 19, 949–959 (2000)
Sumbatyan, M.A., Scalia, A.: Equations of Mathematical Diffraction Theory. CRC Press, Boca Raton (2005)
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The work is performed within the framework of the Project â„– 15-19-10008 of the Russian Science Foundation (RSCF).
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Zotov, V.V., Popuzin, V.V., Tarasov, A.E. (2017). An Experimental Model of the Ultrasonic Wave Propagation Through a Doubly-Periodic Array of Defects. In: Sumbatyan, M. (eds) Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials . Advanced Structured Materials, vol 59. Springer, Singapore. https://doi.org/10.1007/978-981-10-3797-9_11
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DOI: https://doi.org/10.1007/978-981-10-3797-9_11
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