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Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

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Abstract

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

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Acknowledgements

Ms. P. SINGH conveys her sincere thanks to Indian Institute of Technology (Indian School of Mines), Dhanbad, India for providing Junior Research Fellowship.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, 826007, India

    P. Singh, A. Chattopadhyay & A. K. Singh

Authors
  1. P. Singh
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  2. A. Chattopadhyay
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  3. A. K. Singh
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Correspondence to P. Singh.

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Citation: Singh, P., Chattopadhyay, A., and Singh, A. K. Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress. Applied Mathematics and Mechanics (English Edition), 39(3), 317–334 (2018) https://doi.org/10.1007/s10483-018-2306-9

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Singh, P., Chattopadhyay, A. & Singh, A.K. Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress. Appl. Math. Mech.-Engl. Ed. 39, 317–334 (2018). https://doi.org/10.1007/s10483-018-2306-9

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  • DOI: https://doi.org/10.1007/s10483-018-2306-9

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