• Honam Mathematical Journal
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• v.45 no.4
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• pp.668-677
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• 2023

In this study, we bring forth a new general formula for inextensible flows of Euclidean curves as regards modified orthogonal frame (MOF) in E³. For an inextensible curve flow, we provide the necessary and sufficient conditions, which are denoted by a partial differential equality containing the curvatures and torsion.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.805-812
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• 2021

In this study, we obtain various conditions for the non-null curve flows to be inextensible in the 6-dimensional Lorentzian space 𝕃⁶. Then, we find partial differential equations which characterize the family of inextensible non-null curves.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.66-69
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• 2006

In the present study, we propose a virtual boundary method for simulation of massive inextensible flexible strings immersed in viscous fluid flow. The fluid motion is governed by the Navier-Stokes equations and a momentum forcing is added in order to bring the fluid to move at the same velocity with the immersed surface. A massive inextensible flexible string model is described by another set of equations with an additional momentum forcing which is a result of the fluid viscosity and the pressure difference across the string. The momentum forcing is calculated by a feedback loop. Simulations of several numerical examples are carried out, inlcuding a hanging string which starts moving under gravity without ambient fluid, a string swimming within a uniform flow and a uniform flow over two side-by side strings. The numerical results agree well with the theoretical analysis and previous experimental observations. Preliminary results of a swimming elongated fishlike body will also be presented.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.153-161
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• 2019

In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.2
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• pp.198-208
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• 1995

Combining Iwan-Blevin's model into the approximated form of the nonlinear model derived for the dynamic analysis of the riser system with the inclusion of internal flow, current-vortex model is developed to investigate the effect of internal flow on vortex-induced vibration due to inline current The riser system includes a steadly flow inside the pipe which is modeled as an extensible or inextensible tubular beam. Galerkin's finite element approximation are implemented to derive the matrix equation of equilibrium for the finite element system. The investigations of the effect of internal flow on vibration due to inline current are performed according to the change of various parameters such as top tension, infernal flow velocity. current velocity, and so on. It is found that the effect of internal flow on vibration due to vortex shedding can be controlled by the increase of top tension. However, careful consideration has to be given, in design point in order to avoid the resonance band occurding near vortex shedding frequency, particularly for the long riser.

• 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.