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.

中文翻译：

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Biot 粘度扩展理论框架内的无限完全饱和多孔弹性圆柱体的扭转波

摘要 理解波如何在多孔弹性介质中传播的影响是巨大的。多孔弹性圆柱体已用于不同领域的多种应用。例如，地球物理学、结构力学、医学、空气动力学、纳米科学等。这项工作基于 Biot 粘度扩展理论，研究了无限完全饱和、轴对称、多孔弹性圆柱体的扭转振动。当考虑无应力边界条件时，可以得到两个复杂的频率方程：一个与快 S 波相关，另一个与慢 S 波相关。挑战之一是从频率方程中找到相速度和衰减的解析表达式。在这项工作中，获得了这些表达式，并与对应于 Biot 理论的那些表达式进行了比较。当将结果与两种理论框架进行比较时，正如预期的那样，扭转波在 Biot 粘度扩展理论框架中衰减得更多。慢 S 波的影响导致扭转波的传播速度比 Biot 的理论框架慢。