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.
Highlights
Waves propagation in the elastic media is an interesting topic for numerus scientists due to the needs of the complete understanding of different medium characteristics
We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form
The result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation
Summary
Waves propagation in the elastic media is an interesting topic for numerus scientists due to the needs of the complete understanding of different medium characteristics. The existence of dissipation and initial stresses are common occurred in Earth crust Such existence play an important role on the vibrational analysis of torsional wave propagation [29,30,31,32]. It is obvious that the dissipation and the initial stress parameter influences the behavior of the torsional wave propagation in a cylindrical shell. It is of great importance to study propagation of torsional wave in a dissipative cylindrical shell incorporating initial stress effects. The present work proposed a new method to analysis the impacts of initial stress and medium‘s dissipation on the phase velocities of torsional wave propagation in a pre-stressed, dissipative, incompressible cylindrical shell. The analysis are carried based on Biot’s incremental deformation theory
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