Mathematical analysis on the diffraction of shear waves in an initially stressed dry sandy medium by a rigid strip

Abstract

The present study investigates the diffraction of horizontally polarized shear wave (SH-wave) by a rigid strip in an initially-stressed dry sandy infinite-medium. The far-field solution for the diffracted displacement due to shear wave is obtained in closed-form and studied. The patterns of diffraction for displacement in an initially-stressed dry sandy infinite-medium are numerically calculated, and its dependency on wave number is illustrated graphically. The present analysis also describes a noticeable effect of different prevalent parameters, viz., horizontal and vertical initial stresses, sandiness parameter, shear wave speed, and incident angle on diffracted displacement. Furthermore, some particular cases are examined from the obtained expression of diffracted displacement of the shear wave at a significant distance from the rigid strip. Comparative analysis is performed for far-field solution for the diffracted displacement with distinct configurations. Furthermore, the obtained results are matched with pre-established results as a particular case and validation of the problem.

KEYWORDS:

• Diffraction
• dry sandy material
• initial stress
• shear wave
• wave number

Acknowledgments

The authors convey their sincere thanks to School of Basic Sciences, Galgotias University, Greater Noida, Uttar Pradesh and Indian Institute of Technology (Indian School of Mines) Dhanbad for providing the necessary facilities to carry out this research work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data required to reproduce the findings of the present work are available to download from [58].