Finite amplitute oscillations in curvilinearly aeolotropic elastic sylinders

Huilgol, R. R.

doi:10.1090/qam/99895

Cited by 8 publications

(12 citation statements)

References 13 publications

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“…From now on, and to avoid a cumbersome notation, we eliminate the upper bar notation. We note that (27) may easily be integrated once to obtain the first integral…”

Section: Description Of the Bvpmentioning

confidence: 99%

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The rectilinear shear of fiber-reinforced incompressible non-linearly elastic solids

Merodio

Saccomandi

Sgura

2007

International Journal of Non-Linear Mechanics

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“…From now on, and to avoid a cumbersome notation, we eliminate the upper bar notation. We note that (27) may easily be integrated once to obtain the first integral…”

Section: Description Of the Bvpmentioning

confidence: 99%

“…For transversely isotropic materials, Kumar and Chaudury [26] have published a short note dealing with rectilinear shear deformation in which they derive the determining equations for a special constitutive equation previously introduced in [27]. A rectilinear shear deformation is a special case of an antiplane shear deformation.…”

Section: Introductionmentioning

confidence: 99%

The rectilinear shear of fiber-reinforced incompressible non-linearly elastic solids

Merodio

Saccomandi

Sgura

2007

International Journal of Non-Linear Mechanics

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“…The ordinary differential equation (3.8) for the dimensionless inner radius x(t) is valid for radial oscillations in radial, tangential and longitudinal transversely isotropic tubes and has the same form as for radial oscillations in an isotropic tube. It was derived by Huilgol [11] for radial oscillations in a radial transversely isotropic tube. Equation (3.8) applies for general strain-energy function of the form W = W (I 1 ,…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Non-linear radial oscillations in a transversely isotropic incompressible cylindrical tube were first studied by Huilgol [11]. Huilgol considered a radial transversely isotropic tube and derived the conditions on the strain-energy function for the existence of periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Non-linear radial oscillations of a transversely isotropic hyperelastic incompressible tube

Mason

Maluleke

2007

Journal of Mathematical Analysis and Applications

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The constitutive equation for a transversely isotropic incompressible hyperelastic material is written in a covariant form for arbitrary orientation of the anisotropic director. Three non-linear differential equations are derived for radial oscillations in radial, tangential and longitudinal transversely isotropic thin-walled cylindrical tubes of generalised Mooney-Rivlin material. A Lie point symmetry analysis is performed. The conditions on the strain-energy function and on the net applied surface pressure for Lie point symmetries to exist are determined. For radial and tangential transversely isotropic tubes the differential equations are reduced to Abel equations of the second kind. Radial oscillations in a longitudinal transversely isotropic tube and in an isotropic tube are described by the Ermakov-Pinney equation.

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“…On the other hand, the influence of material anisotropy on the large-amplitude vibrations of hyperelastic shells has received much less attention. The first paper on this topic was published by Huilgol [22], who studied the problem of axisymmetric oscillations of an infinitely long cylindrical thick-walled tube, which was curvilinearly transverse-isotropic, i.e., the anisotropy was assumed to exist in the radial direction. The author derived the conditions that strain-energy functions must satisfy for the existence of periodic solutions.…”

Section: Introductionmentioning

confidence: 99%