Vibration analysis of a poroelastic composite hollow sphere

Shanker, B.; Nath, C. Nageswara; Shah, Syed Ahmed; Kumar, J. Manoj

doi:10.1007/s00707-012-0762-5

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…They showed that toroidal motion gets decoupled from rest of the motion and remains unaffected to temperature variations along with some other particular cases. Shanker et al [7] presented the analysis of poroelastic composite hollow spheres along with particular cases wherein rigid core and casing are considered.…”

Section: Introductionmentioning

confidence: 99%

Torsional Vibrations of Coated Hollow Poroelastic Spheres

Shah¹,

Nageswaranath²,

Modem³

et al. 2017

OJA

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Torsional vibrations of coated hollow poroelastic spheres are studied employing Biot's theory of wave propagation in poroelastic solid. The dilatations of solid and liquid media are zero, therefore the frequency equation of torsional vibrations is same both for a permeable and an impermeable surface. The coated poroelastic sphere consists of an inner hollow poroelastic sphere bounded by and bonded to a sphere made of distinct poroelastic material. The inner sphere is designated as core and outer sphere as casing. Core and casing are bonded at the curved surfaces. The inner and outer boundaries of the coated hollow poroelastic sphere are free from stress and at the interface of core and casing the displacement and stresses are continuous. It is assumed that the each material of coated sphere is homogeneous and isotropic. The frequency equation of torsional vibrations of a coated poroelastic hollow sphere is obtained when the material of the core vanishes. Also a coated poroelastic solid sphere is obtained as the limiting case of the frequency equation of coated hollow poroelastic sphere when the inner radius of core approaches to zero. Non-dimensional frequency as a function of ratio of thickness of core to that of inner radius of core is determined and analyzed. It is observed that the frequency and dispersion increase with the increase of the thickness of the coating.

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Section: Introductionmentioning

confidence: 99%

Torsional Vibrations of Coated Hollow Poroelastic Spheres

Shah¹,

Nageswaranath²,

Modem³

et al. 2017

OJA

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“…In the paper in [6], radial and rotatory vibrations of fluid-filled and empty poroelastic spherical shells are investigated. Vibration analysis of a poroelastic composite hollow sphere is discussed by Shanker et al [7]. They derived frequency equations for poroelastic composite hollow sphere and a poroelastic composite hollow sphere with rigid core.…”

Section: Introductionmentioning

confidence: 99%

Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

Gurijala

Perati

2014

International Journal of Engineering Mathematics

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This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot's theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

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“…Shah (2008;2011) studied the problems of wave propagation in fluid-filled cylindrical and spherical shells in the absence of dissipation. Recently, Shanker et al (2013) studied the vibrations of composite poroelastic spheres.…”

Section: Introductionmentioning

confidence: 99%

Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

Shah¹,

Hussaini²

2014

International Journal of Applied Mechanics and Engineering

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The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

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Vibration analysis of a poroelastic composite hollow sphere

Cited by 4 publications

References 15 publications

Torsional Vibrations of Coated Hollow Poroelastic Spheres

Torsional Vibrations of Coated Hollow Poroelastic Spheres

Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

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