scholarly journals Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium

2005 ◽  
Vol 12 (2) ◽  
pp. 261-272
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Couple Stress ◽  
Viscoelastic Medium ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Physical Domain ◽  
Viscoelastic Solid ◽  
Eigenvalue Approach ◽  
Time Harmonic ◽  
Concentrated Source ◽  
Displacement Force

Abstract The present study is concerned with the plane strain problem in homogeneous orthotropic micropolar viscoelastic solid. The disturbance due to the time harmonic concentrated source is investigated by employing the eigenvalue approach. Integral transforms have been inverted by a numerical technique to obtain the components of displacement, force stress and couple stress in the physical domain. The results obtained are given and illustrated graphically.

Dynamical Behaviour of Orthotropic Micropolar Elastic Medium

2002 ◽  
Vol 8 (8) ◽  
pp. 1053-1069 ◽  
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Normal Force ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Dynamical Behaviour ◽  
Normal Displacement ◽  
Physical Domain ◽  
Elastic Solids ◽  
Eigenvalue Approach

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to continuous normal and tangential sources are investigated by employing eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities are given and illustrated graphically.

scholarly journals Response due to mechanical source in second axisymmetric problem of micropolar elastic medium

2013 ◽  
Vol 18 (4) ◽  
pp. 1249-1261
Author(s):  
R. Singh
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Axisymmetric Problem ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Physical Domain ◽  
Concentrated Force ◽  
Infinite Space ◽  
Eigen Value ◽  
Displacement Force

Abstract The second axisymmetric problem in a micropolar elastic medium has been investigated by employing an eigen value approach after applying the Laplace and the Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inversed by using a numerical technique to obtain the components of microrotation, displacement, force stress and couple stress in the physical domain. The results for these quantities are given and illustratred graphically.

ON MODELLING THE TRANSITION TO TURBULENCE IN PIPE FLOW

2017 ◽  
Vol 59 (1) ◽  
pp. 1-34 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
MICHAEL A. BRIDESON
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
Type Equation ◽  
Transition To Turbulence ◽  
Eigenvalue Approach ◽  
Cylindrical Pipe ◽  
Full Generality ◽  
Fluid Turbulence ◽  
Linearized Problem ◽  
The Stability

As a possible model for fluid turbulence, a Reiner–Rivlin-type equation is used to study Poiseuille–Couette flow of a viscous fluid in a rotating cylindrical pipe. The equations of motion are derived in cylindrical coordinates, and small-amplitude perturbations are considered in full generality, involving all three velocity components. A new matrix-based numerical technique is proposed for the linearized problem, from which the stability is determined using a generalized eigenvalue approach. New results are obtained in this cylindrical geometry, which confirm and generalize the predictions of previous recent studies. A possible mechanism for the transition to turbulent flow is discussed.

Elastodynamic Response of a Three-Phase-Lag Model of Orthorhombic Thermoviscoelastic Material with Reference Temperature Dependent Properties

2020 ◽  
Vol 08 (01n02) ◽  
pp. 2050002
Author(s):  
Leena Rani
Keyword(s):  
Reference Temperature ◽  
Phase Lag ◽  
Physical Domain ◽  
Temperature Dependent ◽  
Eigenvalue Approach ◽  
Coupled Equations ◽  
Three Phase ◽  
Lag Model ◽  
Temperature Dependent Properties ◽  
Thermally Conducting

A three-phase-lag model of a homogeneous thermally conducting orthorhombic thermoviscoelastic material under the effect of the dependence of reference temperature on all elastic and thermal parameters is investigated. The Laplace and Fourier transform and eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations. As an application of the problem, harmonically varying and sinusoidal pulse functions are considered. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made for thermoviscoelastic temperature dependent, thermoviscoelastic and thermoelastic materials, respectively, for different values of time, for temperature gradient boundary.

Interaction due to Mechanical and Thermal Sources in Thermoelastic Half-Space with Voids

2005 ◽  
Vol 11 (4) ◽  
pp. 499-517 ◽  
Author(s):  
Rajneesh Kumar ◽  
Leena Rani
Keyword(s):  
Half Space ◽  
Normal Force ◽  
Volume Fraction ◽  
Thermal Source ◽  
Physical Domain ◽  
Coupled Thermoelasticity ◽  
Time Harmonic ◽  
The Fourier Transform ◽  
Mechanical And Thermal Sources ◽  
Thermal Sources

The dynamic response of a homogeneous, isotropic, thermoelastic half-space with voids subjected to time harmonic normal force and thermal source is investigated by applying the Fourier transform. The displacements, stresses, temperature distribution, and change in volume fraction field obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the voids effect for the theory of coupled thermoelasticity and uncoupled thermoelasticity for an insulated boundary and temperature gradient boundary.

Analysis to Stress Relaxation Phenomena of Viscoelastic Materials by Means of Irreversible Thermodynamics (Ⅰ)

2005 ◽  
Vol 297-300 ◽  
pp. 365-370
Author(s):  
Guang Ze Dai ◽  
Lanying Yu ◽  
Jian Ke ◽  
Qing Qing Ni
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Medium ◽  
Stable Equilibrium ◽  
Uniaxial Stress ◽  
Thermodynamic System ◽  
Irreversible Thermodynamics ◽  
Stable Equilibrium State ◽  
Viscoelastic Solid ◽  
Solid Materials ◽  
Generalized Coordinates

Through defining a piece of viscoelastic medium as a thermodynamic system described by the generalized coordinates in the stress relaxation process, the evolution equation is derived by making use of the 1st law of thermodynamics, the 2nd law of thermodynamics and the Onsager’s principle. Based on the general solutions of the evolution, the constitutive expressions of uniaxial stress relaxation are obtained for both ideal viscoelastic solid materials and ideal viscoelastic fluid one respectively, in terms of the situation whether the coordinates participating in the entropy production are in stable or neutrally stable equilibrium state. As the result, whether the stress relaxes to a constant or zero depends on whether the free energy in viscoelastic medium is left or not.

scholarly journals On Lamb's plane problem in micropolar viscoelastic half-space with stretch

1990 ◽  
Vol 13 (2) ◽  
pp. 363-372 ◽  
Author(s):  
Rajneesh Kumar ◽  
M. L. Gogna ◽  
Lokenath Debnath
Keyword(s):  
Half Space ◽  
Plane Problem ◽  
Couple Stress ◽  
Normal Load ◽  
Horizontal Force ◽  
Stress Couple ◽  
Rate Dependent ◽  
Time Harmonic ◽  
Special Cases ◽  
First Moment

A study is made of Lamb's plane problem in micropolar viscoelastic half-space with stretch. The viscoelasticity is characterized by the rate-dependent theories of micro-viscoelasticity generalizing the classical Kelvin-Voigt theory. The displacement components, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load. Two particular cases of a horizontal force and a torque which are time harmonic have been considered. Several limiting cases are obtained as special cases of the present analysis.

scholarly journals Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid

2019 ◽  
Vol 8 (1) ◽  
pp. 39-45
Author(s):  
Vishwanath B. Awati ◽  
Krishna B. Chavaraddi ◽  
Priya M. Gouder
Keyword(s):  
Surface Tension ◽  
Couple Stress ◽  
Numerical Technique ◽  
Taylor Instability ◽  
Couple Stress Fluid ◽  
Nonlinear Saturation ◽  
Roughness Effects ◽  
Two Fluids ◽  
Rayleigh Taylor Instability ◽  
Boundary Roughness

Abstract The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.

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