Torsional waves of infinite fully saturated poroelastic cylinders within the framework of Biot viscosity-extended theory

Abstract The repercussion of understanding how waves propagate in poroelastic media is enormous. Poroelastic cylinders have been used in several applications of different fields. For example, geophysics, structural mechanics, medicine, aerodynamic, nanoscience, among others. This work, based on Biot viscosity-extended theory, investigates the torsional vibrations of infinite fully saturated, axial-symmetric, poroelastic cylinders. Two complex frequency equations are obtained when the stresses-free boundary conditions are taking into account: one associated with the fast S wave and another to the slow S wave. One of the challenges is finding the analytical expressions for phase velocity and attenuation from the frequency equation. In this work, these expressions were obtained and compared with those corresponding to the Biot theory. When comparing the results with both theoretical frameworks, as expected, the torsional waves were attenuated more in the Biot viscosity-extended theory framework. The influence of the slow S wave causes the torsional waves to travel slower than Biot’s theoretical framework.