Effect of rigid boundary on Rayleigh wave in an incompressible heterogeneous medium over an incompressible half-space

Anup Kumar Mukhopadhyay; Asit Kumar Gupta; Santimoy Kundu; Pulak Patra; Anup Kumar Mukhopadhyay; Asit Kumar Gupta; Santimoy Kundu; Pulak Patra

doi:10.3934/math.2020138

AIMS Mathematics

2020, Volume 5, Issue 3: 2088-2099. doi: 10.3934/math.2020138

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Effect of rigid boundary on Rayleigh wave in an incompressible heterogeneous medium over an incompressible half-space

1.
Department of Information Technology, Asansol Engineering College, Asansol
2.
Department of Physics, Asansol Engineering College, Asansol
3.
Department of Applied Mathematics, IIT(ISM), Dhanbad
4.
Department of Mathematics, Brainware Group of Institutions-SDET, Kolkata

Received: 24 September 2019 Accepted: 20 January 2020 Published: 25 February 2020
MSC : 86A15

In the present problem, an attempt has been made to study the propagation of Rayleigh waves in an incompressible medium with polynomial variation (m) of rigidity over an incompressible half-space under rigid layer. Instead of using the Whittaker function, the expansion formula proposed by Newlands has been used for a better result in shallow depth. The velocity equation has been calculated and the results are shown in figures. The study in the assumed medium, the authors obtained that the phase velocity of Rayleigh waves increases except for the polynomial variation of rigidity m = 1, 2 and 3.
- heterogeneity,
- incompressible,
- rigidity,
- rigid boundary,
- wave propagation
Citation: Anup Kumar Mukhopadhyay, Asit Kumar Gupta, Santimoy Kundu, Pulak Patra. Effect of rigid boundary on Rayleigh wave in an incompressible heterogeneous medium over an incompressible half-space[J]. AIMS Mathematics, 2020, 5(3): 2088-2099. doi: 10.3934/math.2020138

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Abstract

In the present problem, an attempt has been made to study the propagation of Rayleigh waves in an incompressible medium with polynomial variation (m) of rigidity over an incompressible half-space under rigid layer. Instead of using the Whittaker function, the expansion formula proposed by Newlands has been used for a better result in shallow depth. The velocity equation has been calculated and the results are shown in figures. The study in the assumed medium, the authors obtained that the phase velocity of Rayleigh waves increases except for the polynomial variation of rigidity m = 1, 2 and 3.

References

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