Reflection of longitudinal wave in the micropolar elasticity with voids. (English) Zbl 07341994
Summary: By considering no more interaction between wryness tensor and change in voids volume fraction in the materials, the reflection problem of plane longitudinal waves at a free boundary of micropolar elastic materials with voids has been investigated. We have obtained the amplitude and energy ratios of reflected waves for the incident longitudinal wave by using appropriate boundary conditions. The effect of void parameters in the nondimensional wavenumber, amplitude and energy ratios are computed numerically for the particular material’s model.
References:
| [1] | Achenbach, J. D. [1976] Wave Propagation in Elastic Solids (North-Holland Publishing Company, New York). · Zbl 0268.73005 |
| [2] | Ariman, T. [1972] “ Wave propagation in a micropolar elastic half-space,” Acta Mech.13, 11-20. · Zbl 0255.73038 |
| [3] | Barak, M. S. and Kaliraman, V. [2018] “ Propagation of elastic waves at micropolar viscoelastic solid/fluid saturated incompressible porous solid interface,” Int. J. Comput. Meth.15, 1850076. · Zbl 1404.74038 |
| [4] | Boschi, E. [1973] “ Lamb and Love wave-propagation in an infinite micropolar thermoelasticity,” Meccanica7, 154-157. · Zbl 0273.73003 |
| [5] | Chandrasekharaiah, D. S. [1986] “ Surface waves in an elastic half-space with voids,” Acta Mech.62, 77-85. · Zbl 0602.73022 |
| [6] | Chandrasekharaiah, D. S. [1987] “ Rayleigh-Lamb waves in elastic plate with voids,” J. Appl. Mech.54, 509-512. · Zbl 0618.73017 |
| [7] | Chirita, S., Ciarletta, M. and Straughan, B. [2006] “ Structural stability in porous elasticity,” Proc. R. Soc. London Ser. A462, 2593-2605. · Zbl 1149.74329 |
| [8] | Chirita, S. and Ghiba, I. D. [2010] “ Inhomogeneous plane waves in elastic materials with voids,” Wave Motion47, 333-342. · Zbl 1231.35057 |
| [9] | Ciarletta, M., Chirita, S. and Passarella, F. [2005] “ Some results on the spatial behavior in linear porous elasticity,” Arch. Mech.57, 43-65. · Zbl 1104.74024 |
| [10] | Ciarletta, M. and Iesan, D. [1993] Non-Classical Elastic Solids (Longman Group of UK Limited, England). · Zbl 0790.73002 |
| [11] | Ciarletta, M., Svanadze, M. and Buonanno, L. [2009] “ Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids,” Eur. J. Mech. A-Solids28, 897-903. · Zbl 1167.74455 |
| [12] | Ciarletta, M. and Straughan, B. [2006] “ Poroacoustic acceleration waves,” Proc. R. Soc. London Ser. A462, 3493-3499. · Zbl 1149.74345 |
| [13] | Ciarletta, M. and Sumbatyan, M. A. [2003] “ Reflection of plane waves by the free boundary of a porous elastic half-space,” J. Sound Vib.259, 253-264. |
| [14] | Cowin, S. C. and Nunziato, J. W. [1983] “ Linear theory of elastic materials with voids,” J. Elast.13, 125-147. · Zbl 0523.73008 |
| [15] | Cruz, V., Hube, J. and Spanos, T. J. T. [1992] “ Reflection and transmission of seismic waves at the boundaries of porous media,” Wave Motion16, 323-338. |
| [16] | Dey, S. and Gupta, S. [1987] “ Longitudinal and shear waves in an elastic medium with void pores,” Proc. Indian Natl. Sci. Acad.53, 554-563. · Zbl 0621.73027 |
| [17] | Eringen, A. C. and Suhubi, E. S. [1964a] “ Non-linear theory of simple microelastic solids-I,” Int. J. Eng. Sci.2, 189-203. · Zbl 0138.21202 |
| [18] | Eringen, A. C. and Suhubi, E. S. [1964b] “ Non-linear theory of simple microelastic solids-II,” Int. J. Eng. Sci.2, 389-404. |
| [19] | Eringen, A. C. [1966] “ Linear theory of micropolar elasticity,” J. Math. Mech.15, 909-924. · Zbl 0145.21302 |
| [20] | Eringen, A. C. [1984] “ Plane waves in nonlocal micropolar elasticity,” Int. J. Eng. Sci.22, 1113-1121. · Zbl 0564.73029 |
| [21] | Eringen, A. C. [1990] “ Theory of thermo-microstrech elastic solid,” Int. J. Eng. Sci.28, 1291-1301. · Zbl 0718.73014 |
| [22] | Gauthier, R. D. [1982] “ Experimental investigation on micropolar media,” in Mechanics of Micropolar Media, eds. Brien, O. and Hsieh, R. K. (World Scientific, Singapore). |
| [23] | Giorgio, I., De Angelo, M., Turco, E. and Misra, A. [2019] “ A Biot-Cosserat two-dimensional elastic nonlinear model for a micromorphic medium,” Contin. Mech. Thermodyn.32, 1357-1369. |
| [24] | Gharahi, A. and Schiavone, P. [2019] “ Uniqueness of solution for plane deformations of a micropolar elastic solid with surface effects,” Contin. Mech. Therm.32, 9-22. · Zbl 1443.74142 |
| [25] | Goodmann, M. A. and Cowin, S. C. [1972] “ A continuum theory for granular materials,” Arch. Rat. Mech. Anal.44, 249-266. · Zbl 0243.76005 |
| [26] | Hassanpour, S. and Heppler, G. L. [2015] “ Micropolar elasticity theory: A survey of linear isotropic equations, representative notations, and experimental investigations,” Math. Mech. Solids22, 224-248. · Zbl 1371.74012 |
| [27] | Iesan, D. [2004] Thermoelastic Models of Continua (Kluwer, Dordrecht). · Zbl 1108.74004 |
| [28] | Kaur, G., Singh, D. and Tomar, S. K. [2018] “ Rayleigh-type wave in nonlocal elastic solid with voids,” Eur. J. Mech. A-Solids71, 134-150. · Zbl 1406.74353 |
| [29] | Kaur, G., Singh, D. and Tomar, S. K. [2019] “ Love wave in a non local elastic media with voids,” J. Vib. Control25, 1470-1483. |
| [30] | Kumar, R. and Choudhary, S. [2003] “ Interaction due to mechanical sources in micropolar elastic medium with voids,” J. Sound Vib.266, 889-904. · Zbl 1236.74295 |
| [31] | Kumar, R. and Deswal, S. [2000] “ Wave propagation in micropolar liquid-saturated porous solid,” Indian J. Pure Appl. Mat.31, 1317-1337. · Zbl 0986.74043 |
| [32] | Kumar, R. and, Deswal, S. [2006] “ Some problems of wave propagation in a micropolar elastic medium with voids,” J. Vib. Control12, 849-879. · Zbl 1182.74130 |
| [33] | Lianngenga, R. [2016] “ Theory of micropolar thermoelastic materials with voids,” IJPAMS9, 1-8. |
| [34] | Lianngenga, R. [2017] “ Effect of inertial coefficients in the propagation of plane waves in micropolar porous materials,” Int. J. Comp. Mat. Sc. Eng.6, 1750007. · Zbl 1480.74014 |
| [35] | Lianngenga, R. and Lalawmpuia [2015] “ Micropolar elasticity containing voids,” IJISET2, 838-844. |
| [36] | Lianngenga, R., Lalvohbika, J. and Lalawmpuia [2018] “ Reflection of P- and S- wave at the interface of micropolar elasticity and thermoelasticity with voids,” J. Mol. Eng. Mat.6, 1850005. |
| [37] | Lianngenga, R. and Singh, S. S. [2019] “ Symmetric and anti-symmetric vibrations in micropolar thermoelastic materials plate with voids,” Appl. Math. Model.76, 856-866. · Zbl 1481.74272 |
| [38] | Marin, M. [1996] “ Some basic theorems in elastostatics of micropolar materials with voids,” J. Comput. Appl. Math.70, 115-126. · Zbl 0853.73003 |
| [39] | Marin, M. [2007] “ On the nonlinear theory of micropolar bodies with voids,” J. Appl. Mech.2007, 15745. · Zbl 1141.74007 |
| [40] | Mirzajani, M., Khaji, N. and Hori, M. [2018] “ Stress wave propagation analysis in one dimensional micropolar rods with variable cross section using micropolar wave finite method,” Int. J. Appl. Mech.10, 1850039. |
| [41] | Mondal, A. K. and Acharya, D. P. [2006] “ Surface waves in a micropolar elastic solids containing voids,” Acta Geophys.54, 430-452. |
| [42] | Nunziato, J. W. and Cowin, S. C. [1979] “ A non linear theory of elastic materials with voids,” Arch. Rat. Mech. Anal.72, 175-201. · Zbl 0444.73018 |
| [43] | Parfitt, V. R. and Eringen, A. C. [1969] “ Reflection of plane waves from the flat boundary of a micropolar elastic half space,” J. Acaust. Soc. Am.45, 1258-1272. |
| [44] | Puri, P. and Cowin, S. C. [1985] “ Plane waves in linear elastic materials with voids,” J. Elast.15, 167-183. · Zbl 0564.73027 |
| [45] | Sharma, M. D. [2012] “ Rayleigh waves in a dissipative poro-visoelastic media,” Bull. Seismol. Soc. Am.102, 2468-2483. |
| [46] | Singh, D., Kaur, G. and Tomar, S. K. [2019] “ Wave in a non local elastic media with voids,” J. Elast.128, 85-114. · Zbl 1373.74051 |
| [47] | Singh, J. and Tomar, S. K. [2006] “ Reflection and refraction of transverse waves at a plane interface between two different porous elastic solid half-spaces,” Appl. Math. Comput.176, 364-378. · Zbl 1131.74315 |
| [48] | Singh, J. and Tomar, S. K. [2007] “ Plane waves in a rotating micropolar elastic solid,” J. Appl. Phys.102, 074906. |
| [49] | Singh, S. S. and Lianngenga, R. [2017] “ Effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids,” Appl. Math. Model.49, 487-497. · Zbl 1480.74014 |
| [50] | Straughan, B. [2008] Stability and Wave Motion in Porous Media (Springer, New York). · Zbl 1149.76002 |
| [51] | Tomar, S. K. [2005] “ Wave propagation in micropolar elastic plate with voids,” J. Vib. Control11, 849-863. · Zbl 1182.74135 |
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