Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (3): 327-338.doi: https://doi.org/10.1007/s10483-011-1418-6

• Articles • 上一篇    下一篇

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

S. GUPTA, A. CHATTOPADHYAY, D. K. MAJHI   

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India
  • 收稿日期:2010-05-07 出版日期:2011-02-28 发布日期:2011-03-01

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

S. GUPTA, A. CHATTOPADHYAY, D. K. MAJHI   

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India
  • Received:2010-05-07 Online:2011-02-28 Published:2011-03-01

摘要: The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.

Abstract: The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.

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