• Korea-Australia Rheology Journal
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• v.14 no.1
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• pp.33-45
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• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.1
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• pp.75-90
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• 1995

A mathematical model for the dynamic analysis of a riser system with the inclusion of internal flow and nonlinear effects due to large structural displacements is developed to investigate the effect of internal flow on marine riser dynamics. The riser system accounts fir the nonlinear boundary conditions and includes a steady flow inside the pipe which is modeled as an extensible or inextensible. tubular beam subject to nonlinear three dimensional hydrodynamic loads such as current or wave excitation. Galerkin's finite element approximation and time incremental operator are implemented to derive the matrix equation of equilibrium for the finite element system and the extensibility or inextensibility condition is used to reduce degree of freedom of the system and the required computational time in the case of a nonlinear model. The algorithm is implemented to develop computer programs used in several numerical applications. The investigations of the effect of infernal flow on riser vibration due to current or wave loading are performed according to the change of various parameters such as top tension, internal flow velocity, current velocity, wave period, and so on. It is found that the effect of internal flow can be controlled by the increase of top tension. However, careful consideration has to be given in the design point particularly for the long riser under the harmonic loading such as waves. And it is also found that the consideration of nonlinear effects due to large structural displacements increases the effect of internal flow on riser dynamics.

• Journal of the Korean Magnetics Society
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• v.9 no.6
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• pp.271-277
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• 1999

Amorphous $Fe_{83}B_9Nb_7Cu_1$ alloy has been studied by M$\"{o}$ssbauer spectroscopy. Revised Vincze method was used and distributions of hyperfine field, isomer shift, and quadrupole line broadening of the sample at various temperatures have been evaluated and Curie temperature and $H_{hf}\;(0)$ were calculated to be 393 K and 231 kOe, respectively. Temperature variation of reduced average hyperfine field shows a flattered curvein comparison with the Brillouin curve for S=1. This behavior can be explained on the basis of Handrich molecular field model, in which the parameter Δ, which is a measure of fluctuation in exchange interactions, is assumed to have the temperature dependence ${Delta}=0.75-0.64{\tau}+0.47{\tau}^2$ where $\tau$ is $T/T_C$. At low temperature, the average hyperfine field can be fitted to $H_{hf}\;(T)=H_{hf}\;(0)\;[1-0.44\;(T/T_C)^{3/2}-0.28(T/T_C)^{5/2}-… ]$, which indicates the presence long wave length spin wave excitations. At temperature near TC, reduced average hyperfine field varies as $1.00\;[1-T/T_C]^{0.39}$. It is also found that half-width of the hyperfine field distribution was 102 kOe (3.29 mm/s) at 13 K and decreased monotonically as temperature increased. Above the Curie temperature, an average quadrupole splitting value of 0.43 mm/s was found. Average line broadening due to quadrupole splitting distribution was 0.31 mm/s at 13 K and decreases monotonically to 0.23 mm/s at 320 K, whereas that due to the isomer shift distribution is 0.1 mm/s at 13 K and 0.072 mm/s at 320 K, which is much smaller than that of both hyperfine field and quadrupole splitting. The temperature dependence of the isomer shift can be fitted within the harmonic approximation to a Deybe model with a Debye temperature ${Theta}_D=424{\pm}5K$.TEX>.