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Impact of Torsional Waves in Dry Sandy Desert with Sand Dunes

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Abstract

Aim

The study is to investigate the impact of torsional surface wave in dry sand-filled desert whose upper surface is irregular due to transverse sand dunes.

Method and Consideration

In the desert, the rigidity and density of the granular soil are presumed to vary in an exponential form with the depth of it. The free surface of the desert has been contemplated as I) traction frees, II) rigid boundary. The four scattering equations for the cases are obtained in a closed form by means of separation variables method in the presence of Whittaker differential equation. Some special cases are derived, and their existence has been discussed. The influences of inhomogeneity factor, irregularity of dunes and sandy parameter on the phase velocity have also been studied graphically in the cases.

Purpose

The result is useful to realize geo-dynamics of the sandy desert, earthquake engineering, civil engineering construction of road and building on the sandy medium, oil exploration, artificial exploration, etc.

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Abbreviations

E :

Young’s modulus of medium

σ 1 :

Poisson’s ratio

η :

Sandiness factor of desert

µ :

Rigidity of the medium

ρ :

Density of the medium

λ :

Lame’s parameter

2d :

Span of the irregularity

g :

Standard gravitational acceleration

Ω :

Dilatation

σ ij :

Stress components

e ij :

Strain components

∂ij :

Kronecker delta

G :

Biot’s gravity arbitrary constant

ω :

Angular frequency

β 0 :

Shear wave velocity

J n(Kr):

Bessel’s functions of first kind of order n

Y n(Kr):

Bessel’s functions of second kind of order n

\(W_{{\frac{m}{2\sqrt n },0}}\) :

Whittaker function

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Acknowledgements

The authors would like to thank the Department of Applied Mathematics, IIT (ISM), Dhanbad, India, for providing the best research facilities.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand, 826004, India

    Pasupati Paul & Santimoy Kundu

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  1. Pasupati Paul
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  2. Santimoy Kundu
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Correspondence to Pasupati Paul.

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Paul, P., Kundu, S. Impact of Torsional Waves in Dry Sandy Desert with Sand Dunes. J. Vib. Eng. Technol. 9, 1211–1222 (2021). https://doi.org/10.1007/s42417-021-00291-0

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  • DOI: https://doi.org/10.1007/s42417-021-00291-0

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