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# Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

Mahmoud M. Selim1,2,*, Khaled A. Gepreel3
1 Department of Mathematics-College of Sciences & Humanities in Al Aflaj, Prince Sattam bin Abdulaziz University, Al-Aflaj, 11912, KSA
2 Department of Mathematics, Suez Faculty of Science, Suez University, Egypt
3 Department of Mathematics, Faculty of Science, Taif University, Taif, 21944, Saudi Arabia
* Corresponding Author: Mahmoud M. Selim. Email:

Computers, Materials & Continua 2022, 70(2), 3021-3030. https://doi.org/10.32604/cmc.2022.019579

Received 18 April 2021; Accepted 01 June 2021; Issue published 27 September 2021

### Abstract

The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot's principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details. We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (δ) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot's incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles.

### Keywords

Propagation; torsional wave; dissipation; cylindrical shell; initial stress

M. M. Selim and K. A. Gepreel, "Torsional wave in a dissipative cylindrical shell under initial stresses," Computers, Materials & Continua, vol. 70, no.2, pp. 3021–3030, 2022.

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