##
**Longitudinal waves at a micropolar fluid/solid interface.**
*(English)*
Zbl 1167.74462

Summary: The possibility of plane wave propagation in a micropolar fluid of infinite extent has been explored. The reflection and transmission of longitudinal elastic wave at a plane interface between a homogeneous micropolar fluid half-space and a micropolar solid half-space has also been investigated. It is found that there can exist four plane waves propagating with distinct phase speeds in an infinite micropolar fluid. All the four waves are found to be dispersive and attenuated. The reflection and transmission coefficients are found to be the functions of the angle of incidence, the elastic properties of the half-spaces and the frequency of the incident wave. The expressions of energy ratios have also been obtained in explicit form. Frequency equation for the Stoneley wave at micropolar solid/fluid interface has also been derived in the form of sixth-order determinantal expression, which is found in full agreement with the corresponding result of inviscid liquid/elastic solid interface. Numerical computations have been performed for a specific model. The dispersion curves and attenuation of the existed waves in micropolar fluid have been computed and depicted graphically. The variations of various amplitudes and energy ratios are also shown against the angle of incidence. Results of some earlier workers have been deduced from the present formulation.

### MSC:

74J15 | Surface waves in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

PDFBibTeX
XMLCite

\textit{D. Singh} and \textit{S. K. Tomar}, Int. J. Solids Struct. 45, No. 1, 225--244 (2008; Zbl 1167.74462)

Full Text:
DOI

### References:

[1] | Achenbach, J. D.: Wave propagation in elastic solids, (1973) · Zbl 0268.73005 |

[2] | Ainslie, M. A.; Burns, P. W.: Energy conserving reflection and transmission coefficients for a solid – solid boundary, J. acoust. Soc. am. 98, No. 5, 2836-2840 (1995) |

[3] | Cosserat, E.; Cosserat, F.: Theorie des corps deformables, (1909) · JFM 40.0862.02 |

[4] | Eringen, A. C.: Simple micro-fluids, Int. J. Eng. sci. 2, 205-217 (1964) · Zbl 0136.45003 · doi:10.1016/0020-7225(64)90005-9 |

[5] | Eringen, A. C.: Theory of micropolar fluids, J. math. Mech. 16, 1-18 (1966) · Zbl 0145.21302 |

[6] | Eringen, A. C.: Linear theory of micropolar elasticity, J. math. Mech. 15, 909-924 (1966) · Zbl 0145.21302 |

[7] | Eringen, A. C.: Microcontinuum field theories I: Foundations and solids, (1999) · Zbl 0953.74002 |

[8] | Ewing, W. M.; Jardetzky, W. S.; Press, F.: Elastic waves in layered media, (1957) · Zbl 0083.23705 |

[9] | Hsia, S. Y.; Cheng, J. W.: Longitudinal plane wave propagation in elastic-micropolar porous media, Jpn. J. Appl. phys. 45, No. 3A, 1743-1748 (2006) |

[10] | Kumar, R.; Tomar, S. K.: Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface, Int. J. Math. math. Sci. 26, No. 11, 658-694 (2001) · Zbl 1043.74026 · doi:10.1155/S0161171201005415 |

[11] | Mindlin, R. D.: Micro-structure in linear elasticity, Arch. ration. Mech. anal. 16, 51-78 (1964) · Zbl 0119.40302 · doi:10.1007/BF00248490 |

[12] | Parfitt, V. R.; Eringen, A. C.: Reflection of plane waves from the flat boundary of a micropolar elastic half-space, J. acoust. Soc. am. 45, 1258-1272 (1969) |

[13] | Stoneley, R.: Elastic waves at the surface of separation of two solids, Proc. roy. Soc. lond. 106, 416-428 (1924) · JFM 51.0644.01 |

[14] | Tomar, S. K.; Garg, M.: Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces, Int. J. Eng. sci. 43, No. 1-2, 139-169 (2005) · Zbl 1211.74137 · doi:10.1016/j.ijengsci.2004.08.006 |

[15] | Tomar, S. K.; Kumar, R.: Reflection and refraction of longitudinal displacement wave at a liquid-micropolar solid interface, Int. J. Eng. sci. 33, No. 10, 1507-1515 (1995) · Zbl 0899.73114 · doi:10.1016/0020-7225(95)00015-P |

[16] | Tomar, S. K.; Kumar, R.: Wave propagation at liquid/micropolar elastic solid interface, J. sound vib. 222, No. 5, 858-869 (1999) |

[17] | Tomar, S. K.; Gogna, M. L.: Reflection and refraction of longitudinal wave at an interface between two micropolar elastic solids in welded contact, J. acoust. Soc. am. 97, No. 2, 822-830 (1995) · Zbl 0899.73092 |

[18] | Tomar, S. K.; Singh, D.: Propagation of Stoneley waves at an interface between two microstretch elastic half-spaces, J. vib. Cont. 12, 995-1009 (2006) · Zbl 1182.74134 · doi:10.1177/1077546306068689 |

[19] | Tajuddin, M.: Existence of Stoneley waves at unbonded interface between two micropolar elastic half spaces, J. appl. Mech. 62, 255-257 (1995) · Zbl 0822.73021 · doi:10.1115/1.2895919 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.