Abstract
This paper is devoted to study of the dispersion equation of Love waves in a fiber-reinforced medium sandwiched between an isotropic layer and elastic half-space under the influence of gravity. The equations of motion have been discussed in each media. The frequency equation of a Love wave was obtained using the separation of variables method and Whittaker’s function expansion under a suitable assumption. The boundary conditions were introduced at interfaces of the upper layer, intermediate medium, and half-space. The dispersion equation was derived in closed form by means of Biot’s gravity parameter. The particular cases have been derived in the absence of reinforcement and gravitational force of the reinforced layer and half-space, respectively. Numerical solutions were discussed graphically to show the nature of wave propagation. Dimensionless phase velocity was obtained against non-dimensional wave number for different values of reinforced parameters, Biot’s gravity parameter, and thickness ratio of the upper layer and intermediate layer.
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Acknowledgments
The authors are thankful to University Grants Commission (UGC), New Delhi, India, for providing financial support to Mr D. K. Pandit under UGC-BSR(UGC-Basic Scientific Research) through Grant No. F.7-79/2007(BSR). Authors are also thankful to the Indian School of Mines, Dhanbad, India, for providing necessary facility for research work.
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Kundu, S., Pandit, D.K., Gupta, S. et al. Love wave propagation in a fiber-reinforced medium sandwiched between an isotropic layer and gravitating half-space. J Eng Math 100, 109–119 (2016). https://doi.org/10.1007/s10665-015-9837-3
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DOI: https://doi.org/10.1007/s10665-015-9837-3