Torsion of an elastic solid cylinder with a radial variation in the shear modulus

1976 ◽  
Vol 6 (3) ◽  
pp. 229-244 ◽  
Author(s):  
O. D. George
Keyword(s):  
Shear Modulus ◽  
Elastic Solid ◽  
Radial Variation ◽  
Solid Cylinder

scholarly journals IV. On double refraction in a viscous fluid in motion

1874 ◽  
Vol 22 (148-155) ◽  
pp. 46-47 ◽  
Keyword(s):  
Internal Friction ◽  
Viscous Fluid ◽  
Polarized Light ◽  
Elastic Solid ◽  
The State ◽  
Solid Cylinder ◽  
Annular Space ◽  
Double Refraction ◽  
Fresh Start ◽  
The Moment

According to Poisson’s theory of the internal friction of fluids, a viscous fluid behaves as an elastic solid would do if it were periodically liquefied for an instant and solidified again, so that at each fresh start it becomes for the moment like an elastic solid free from strain. The state of strain of certain transparent bodies may be investigated by means of their action on polarized light. This action was observed by Brewster, and was shown by Fresnel to be an instance of double refraction. In 1866 I made some attempts to ascertain whether the state of strain in a viscous fluid in motion could be detected by its action on polarized light. I had a cylindrical box with a glass bottom. Within this box a solid cylinder could be made to rotate. The fluid to be examined was placed in the annular space between this cylinder and the sides of the box. Polarized light was thrown up through the fluid parallel to the axis, and the inner cylinder was then made to rotate. I was unable to obtain any result with solution of gum or sirup of sugar, though I observed an effect on polarized light when I compressed some Canada balsam which had become very thick and almost solid in a bottle.

The Elastic Coefficients of the Theory of Consolidation

1957 ◽  
Vol 24 (4) ◽  
pp. 594-601
Author(s):  
M. A. Biot ◽  
D. G. Willis
Keyword(s):  
Nonlinear Systems ◽  
Shear Modulus ◽  
Physical Interpretation ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Fluid Content ◽  
Alternate Forms ◽  
Elastic Coefficients ◽  
Methods Of Measurement

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

scholarly journals Analytical solutions for cosmological perturbations in a one-component universe with shear stress

2015 ◽  
Vol 24 (08) ◽  
pp. 1550063 ◽  
Author(s):  
Matej Škovran
Keyword(s):  
Shear Stress ◽  
Energy Density ◽  
Shear Modulus ◽  
Ideal Fluid ◽  
Analytical Solutions ◽  
Elastic Solid ◽  
Explicit Solutions ◽  
Cosmological Perturbations ◽  
Flat Universe ◽  
Tensor Perturbations

We construct explicit solutions for scalar, vector and tensor perturbations in a less known setting, a flat universe filled by an isotropic elastic solid with pressure and shear modulus proportional to energy density. The solutions generalize the well-known formulas for cosmological perturbations in a universe filled by ideal fluid.

scholarly journals The effect of arbitrarily small rigidity on the free oscillations of the Earth

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Gilbert
Keyword(s):  
Shear Modulus ◽  
Singular Perturbation ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Free Oscillations ◽  
Approximate Methods ◽  
Fluid State ◽  
The Earth ◽  
Elastic Interface ◽  
Small Shear

The system of propagator equations for an elastic solid becomes singular as the shear modulus becomes vanishingly small. In computational applications there is severe loss of precision as the limit of zero shear modulus is approached. The use of perturbation theory to address the effect of very small shear modulus, using the fluid state as a basis, is unsatisfactory because certain phenomena, e.g., Rayleigh waves, cannot be represented. Two approximate methods are presented to account for the singular perturbation. Since most of the Earth is nearly neutrally stratified, in which case the motion is nearly irrotational, one can impose the irrotational constraint and obtain a modified and reduced system of propagator equations. This system does not have the singular perturbation. In the second method the transition zone between a fluid and a solid is represented as an infinitesimally thin, Massive, Elastic Interface (MEI). The boundary conditions across the MEI are dispersive and algebraic. The limit of zero shear modulus is non-singular.

scholarly journals Static, Transient and Free Vibirational analysis of thermo magneto electric elastic solid cylinder

2018 ◽  
Vol 7 (2.21) ◽  
pp. 144
Author(s):  
S Karthikeyan ◽  
T K. Parvatha Varthini
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Free Vibration Analysis ◽  
Elastic Solid ◽  
Wave Number ◽  
Solid Cylinder ◽  
Numerical Work ◽  
Global Dynamic ◽  
Hybrid Numerical Method ◽  
Stiffness And Damping

In this paper the static, transient and free vibration analysis of a thermo- magneto-electric-elastic solid cylinder is analyzed stochastically by using hybrid numerical method (combined finite element and Newmark finite difference method).An infinite solid cylinder made up of 6mm class considered. The constitutive equations containing the mechanical, magnetic, electrical and thermal fields and investigated by free and forced Vibirational boundary conditions. The transient finite element equations are obtained by assumed shape functions. After assembling the Mass, Stiffness and Damping and matrices, the global dynamic equations are in the form of time field. The resulting equations are solved by using the finite difference technique with suitable time instants. By using material constants values the displacement, velocity and acceleration of vibrations are obtained with various time values and the non dimensional frequencies are also obtained by different values of non dimensional wave number. Numerical work is carried out by the electric and magnetic materials Cdse and CoFe2o4. The outcomes are tabulated and represented graphically.  

Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition

2011 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu ◽  
Nick Vaughan
Keyword(s):  
Fourier Series ◽  
Shear Modulus ◽  
Solution Method ◽  
Analytic Solution ◽  
Elastic Solid ◽  
Local Deformation ◽  
Elastic Substrate ◽  
Micro Scale ◽  
Surface Stresses ◽  
Layered Solid

This paper describes a fully analytic solution method for the displacements and sub-surface stresses within a graded elastic layered solid. This method can be utilised to predict the local deformation of nano or micro-scale depositions under contacting conditions. The solid consists of two distinct layers which are considered to be perfectly bonded and comprise of a graded elastic coating whose shear modulus varies exponentially with the depth coordinate and an infinitely deep homogeneously elastic substrate. The solution given in this paper is generic and easily utilised to solve real problems as it requires only known physical characteristics of the solid under study and an applied surface pressure. As a result, this model is very cheap to use and can be easily integrated into tribological codes to predict local deflections.

scholarly journals Shear modulus of an elastic solid under external pressure as a function of temperature: The case of helium

2012 ◽  
Vol 85 (6) ◽  
Author(s):  
Felipe Barra ◽  
Fernando Lund ◽  
Nicolás Mujica ◽  
Sergio Rica
Keyword(s):  
Shear Modulus ◽  
Elastic Solid ◽  
External Pressure
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