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Transformational cloaking from seismic surface waves by micropolar metamaterials with finite couple stiffness. (English) Zbl 1467.86006

Summary: Transformational elastodynamics can be used to protect sensitive structures from harmful waves and vibrations. By designing the material properties in a region around the sensitive structure, a cloak, the incident waves can be redirected as to cause minimal or no harmful response on the pertinent structure. In this paper, we consider such transformational cloaking built up by a suitably designed metamaterial exhibiting micropolar properties. First, a theoretically perfect cloak is obtained by designing the properties of an (unphysical) restricted micropolar material within the surrounding medium. Secondly, we investigate the performance of the cloak under more feasible design criteria, relating to finite elastic parameters. In particular, the behavior of a physically realizable cloak built up by unrestricted micropolar elastic media is investigated. Numerical studies are conducted for the case of buried as well as surface breaking structures in 2D subjected to incident Rayleigh waves pertinent to seismic loading. The studies show how the developed cloaking procedure can be utilized to substantially reduce the response of the structure. In particular, the results indicate the performance of the cloak in relation to constraints on the elastic parameters.

MSC:

86A15 Seismology (including tsunami modeling), earthquakes
74J15 Surface waves in solid mechanics
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[1] Pliny the Elder, Pliny’s natural history, volume X: book 36, XXI, (1954), Harvard University Press Massachusetts, (Translated by D. E. Eichholz)
[2] Brûlé, S.; Javelaud, H.; Enoch, E. S.; Guenneau, S., Experiments on seismic metamaterials: molding surface waves, Phys. Rev. Lett., 112, 133901, (2014)
[3] Greenleaf, A.; Lassas, M.; Uhlmann, G., On nonuniqueness for calderon’s inverse problem, Math. Res. Lett., 10, 685-693, (2003) · Zbl 1054.35127
[4] Pendry, J. B.; Schurig, D.; Smith, D. R., Controlling electromagnetic fields, Science, 312, 1780-1782, (2006) · Zbl 1226.78003
[5] Milton, G. W.; Briane, M.; Willis, J. R., On cloaking for elasticity and physical equations with a transformation invariant form, New J. Phys., 8, 1-21, (2006)
[6] Norris, A. N., Acoustic cloaking theory, Proc. R. Soc. A: Math. Phys. Eng. Sci., 464, 2411-2434, (2008) · Zbl 1186.74060
[7] Vasquez, F. G.; Milton, G. W.; Onofrei, D.; Seppecher, P., Transformational elastodynamics and active exterior acoustic cloaking, (Acoustic Metamaterials, Springer Series in Materials Science, vol. 166, (2013)), 289-318
[8] Norris, A.; Amirkulova, F.; Parnell, W., Active elastodynamic cloaking, Math. Mech. Solids, 19, 603-625, (2014) · Zbl 1298.74126
[9] Norris, A.; Parnell, W., Hyperelastic cloaking theory: transformation elasticity with pre-stressed solids, Proc. R. Soc. A, 468, 2881-2903, (2012) · Zbl 1371.74039
[10] Parnell, W.; Norris, A.; Shearer, T., Employing pre-stress to generate finite cloaks for antiplane elastic waves, Appl. Phys. Lett., 100, 171907, (2012)
[11] Parnell, W., Nonlinear pre-stress for cloaking from antiplane elastic waves, Proc. R. Soc. A, 468, 563-580, (2012) · Zbl 1364.74049
[12] Hu, J.; Chang, Z.; Hu, G., Approximate method for controlling solid elastic waves by transformation media, Phys. Rev. B, 84, (2011)
[13] Farhat, M.; Guenneau, S.; Enoch, S., Ultrabroadband elastic cloaking in thin plates, Phys. Rev. Lett., 103, 024301, (2009)
[14] Brun, M.; Colquitt, D.; Jones, I.; Movchan, A.; Movchan, N., Transformational cloaking and radial approximations for flexural waves in elastic plates, New J. Phys., 16, 093020, (2014)
[15] Colquitt, D.; Brun, M.; Gei, M.; Movchan, A.; Movchan, N., Transformation elastodynamics and cloaking for flexural waves, J. Mech. Phys. Solids, 72, 131-143, (2015) · Zbl 1328.74055
[16] Brun, M.; Guenneau, S.; Movchan, A. B., Achieving control of in-plane elastic waves, Appl. Phys. Lett., 94, 1-3, (2009)
[17] Norris, A. N.; Shuvalov, A. L., Elastic cloaking theory, Wave Motion, 48, 525-538, (2011) · Zbl 1283.74024
[18] Eringen, A., Linear theory of micropolar elasticity, J. Math. Mech., 15, 6, 909-923, (1966) · Zbl 0145.21302
[19] Eremeyev, V. A.; Lebedev, L. P.; Altenbach, H., (Foundations of Micropolar Mechanics, SpringerBriefs in Applied Sciences and Technology, (2013)), 35-66
[20] Olsson, P.; Wall, D. J.N., Partial elastodynamic cloaking by means of fiber-reinforced composites, Inverse Problems, 27, 045010, (2011) · Zbl 1219.35365
[21] Kohn, R.; Shen, H.; Vogelius, M.; Weinstein, M., Cloaking via change of variables in electric impedance tomography, Inverse Problems, 24, 015016, (2008) · Zbl 1153.35406
[22] Colquitt, D.; Jones, I.; Movchan, N.; Movchan, A.; Brun, M.; McPhedran, R., Making waves round a structured cloak: lattices, negative refraction and fringes, Proc. R. Soc. A, 469, (2013)
[23] Olsson, P., The rigid movable inclusion in elastostatics and elastodynamics, Wave Motion, 7, 421-445, (1985) · Zbl 0588.73044
[24] Karlsson, A., Scattering of Rayleigh Lamb waves from a 2D-cavity in an elastic plate, Wave Motion, 6, 205-222, (1984) · Zbl 0534.73022
[25] M. Brun, S. Guenneau, A.B. Movchan, Invisibility to in-plane elastic waves, in: XIX Congresso AIMETA, Ancona, Italy, 14-17 September, 2009.
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