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.

• Publication year

  2021

• Venue

  Applied Mathematics and Computation

• Publication date

  2021-02-15

• Fields of study

  Physics, Computer Science, Engineering

• Identifiers
  DOI 10.1016/J.AMC.2020.125636
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method

  2020cited by this paper
• Overview of Carbon Nanotubes for Biomedical Applications

  2019cited by this paper
• Investigation of three-dimensional theory on sound transmission through compressed poroelastic sandwich cylindrical shell in various boundary configurations

  2019cited by this paper
• Hydrogels as Porogens for Nanoporous Inorganic Materials

  2018cited by this paper
• Viscoelastically coupled dynamics of FG Timoshenko microbeams

  2018cited by this paper
• Effective Biot theory and its generalization to poroviscoelastic models

  2018cited by this paper
• Wave transmission across laminated composite plate in the subsonic flow Investigating Two-variable Refined Plate Theory

  2018cited by this paper
• Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory

  2018cited by this paper
• Multi objective optimization of sound transmission across laminated composite cylindrical shell lined with porous core investigating Non-dominated Sorting Genetic Algorithm

  2017cited by this paper
• Vibroacoustic study on a multilayered functionally graded cylindrical shell with poroelastic core and bonded-unbonded configuration

  2017cited by this paper
• Generalized poroelasticity framework for micro‐inhomogeneous rocks

  2016cited by this paper
• Three dimensional sound transmission through poroelastic cylindrical shells in the presence of subsonic flow

  2016cited by this paper
• A mixed "Biot-Shell" analytical model for the prediction of sound transmission through a sandwich cylinder with a poroelastic core

  2016cited by this paper
• A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method

  2016cited by this paper
• Generalized poroviscoelastic model based on effective Biot theory and its application to borehole guided wave analysis

  2016cited by this paper
• Study of radial vibrations in cylindrical bone in the framework of transversely isotropic poroelasticity

  2016cited by this paper
• Investigation of torsional vibrations in thick walled hollow poroelastic cylinder using Biot’s extension theory

  2015cited by this paper
• Exact results for generalized Biot–Gassmann equations for rocks that change in pore shape and grain geometry

  2015cited by this paper
• Sound transmission through triple-panel structures lined with poroelastic materials

  2015cited by this paper
• The effect of external mean flow on sound transmission through double-walled cylindrical shells lined with poroelastic material

  2014cited by this paper
• Longitudinal vibration analysis for microbars based on strain gradient elasticity theory

  2014cited by this paper
• Biomedical applications of carbon nanotubes

  2013cited by this paper
• A sixth-order compact finite difference method for non-classical vibration analysis of nanobeams including surface stress effects

  2013cited by this paper
• Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models

  2013cited by this paper
• Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories

  2012cited by this paper
• Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation

  2012cited by this paper
• Role of structural anisotropy of biological tissues in poroelastic wave propagation.

  2012cited by this paper
• Free vibration analysis of functionally graded size-dependent nanobeams

  2012cited by this paper
• Shear wave propagation in a layered poroelastic structure

  2012cited by this paper
• Energy partition and resonant excitation of poroelastic waves in the absence of dissipation

  2012cited by this paper
• Torsion of strain gradient bars

  2011cited by this paper
• Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

  2011cited by this paper
• Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress

  2011cited by this paper
• Analysis of dispersion and attenuation of surface waves in poroelastic media in the exploration-seismic frequency band

  2011cited by this paper
• On extensional waves in a poroelastic cylinder within the framework of viscosity-extended Biot theory: the case of traction-free open-pore cylindrical surface

  2009cited by this paper
• Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

  2009cited by this paper
• On the Biot slow S-wave

  2008cited by this paper
• Drained and Undrained Poroelastic Properties of Healthy and Pathological Bone: A Poro-Micromechanical Investigation

  2005cited by this paper
• Amplitude of Biot's slow wave scattered by a spherical inclusion in a fluid-saturated poroelastic medium

  2005cited by this paper
• Seismic attenuation due to wave-induced flow

  2004cited by this paper
• Shock-induced borehole waves in porous formations: Theory and experiments

  2004cited by this paper
• Standing torsional waves in a fully saturated, porous, circular cylinder

  2004cited by this paper
• Seismic wave propagation in inhomogeneous and anisotropic porous media

  2001cited by this paper
• Biot theory: a review of its application to ultrasound propagation through cancellous bone.

  1999cited by this paper
• Dynamic poroelasticity of thinly layered structures

  1998cited by this paper
• SOUND TRANSMISSION THROUGH MULTI-PANEL STRUCTURES LINED WITH ELASTIC POROUS MATERIALS

  1996cited by this paper
• Elastodynamics of deformable porous media

  1996cited by this paper
• Complex Variables and Applications

  1985cited by this paper
• Biot-consistent elastic moduli of porous rocks; low-frequency limit

  1985cited by this paper
• Torsional Vibrations of Poroelastic Cylinders

  1980cited by this paper
• Mathematical Methods for Physicists

  1967cited by this paper
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

  1965cited by this paper
• Three‐Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders. I. Analytical Foundation

  1959cited by this paper
• Three‐Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders. II. Numerical Results

  1959cited by this paper
• Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range

  1956cited by this paper
• Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid

  1956cited by this paper
• Torsional vibrations of hollow thin-walled cylindrical beams

  1954cited by this paper
• Bessel Functions. (Scientific Books: A Treatise on the Theory of Bessel Functions)

  1923cited by this paper

• Analytical Study of Torsional Wave Behavior in Graded Poroelastic Layer Bonded to Viscoelastic Foundation

  2025cites this paper
• On torsional vibrations of infinite axial-symmetric dry and air-saturated poroelastic cylinders

  2025influential citation
• S $$^4$$ 4 : simple quasi-1D model for structural health monitoring of single lap joint software

  2023cites this paper
• On torsional vibrations of axial-symmetric infinite hollow poroelastic cylinders

  2022cites this paper
• On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

  2021cites this paper