• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.11a
• /
• pp.600-605
• /
• 2004

In many machines handling lightweight and flexible media such as magnetic tape drives, xerographic copiers and sewing machines, the media must transit an open space. It is important to predict the static and dynamic behavior of the sheets with a high degree of reliability. The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite differential method. The parametric cubic curve is applied for defining the guide shape. The dynamic contact conditions suggested by Klarbring is used to predict the direction of the flexible media according to the initial velocity and the friction coefficient. The analysis is also compared to the conventional model, showing that after contacting a $45^{\circ}$ wall, the directions of flexible media of two models are different.

• Coupled systems mechanics
• /
• v.12 no.1
• /
• pp.21-40
• /
• 2023

In thisstudy, the vibration problem ofthermo elastic carbon nanotubes conveying pulsating viscous nano fluid subjected to a longitudinal magnetic field is investigated via Euler-Bernoulli beam model. The controlling partial differential equation of motion is arrived by adopting Eringen's non local theory. The instability domain and pulsation frequency of the CNT is obtained through the Galerkin's method. The numerical evaluation of thisstudy is devised by Haar wavelet method (HWM). Then, the proposed model is validated by analyzing the critical buckling load computed in presentstudy with the literature. Finally, the numerical calculation ofsystem parameters are shown as dispersion graphs and tables over non local parameter, magnetic flux, temperature difference, Knudsen number and viscous parameter.

• The Pure and Applied Mathematics
• /
• v.27 no.4
• /
• pp.231-249
• /
• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• The Pure and Applied Mathematics
• /
• v.22 no.2
• /
• pp.159-168
• /
• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.8
• /
• pp.945-956
• /
• 1999

This work reports a set of approximate analytical solutions describing the initial transient process of close-contact melting between a rectangular parallelepiped solid and a flat plate on which either constant temperature or constant heat flux is imposed. Not only relative motion of the solid block tangential to the heating plate, but also the density difference between the solid and liquid phase is incorporated in the model. The thin film approximation reduces the force balance between the solid weight and liquid pressure, and the energy balance at the melting front into a simultaneous ordinary differential equation system. The normalized model equations admit compactly expressed analytical solutions which include the already approved two-dimensional solutions as a subset. In particular, the normalized liquid film thickness is independent of all pertinent parameters, thereby facilitating to define the transition period of close-contact melting. A unique behavior of the solid descending velocity due to the density difference is also resolved by the present solution. A new geometric function which alone represents the three-dimensional effect is introduced, and its properties are clarified. One of the representative results is that heat transfer is at least enhanced at the expense of the increase in friction as the cross-sectional shape deviates from the square under the same contact area.

• Journal of the Korean Society of Environmental Restoration Technology
• /
• v.9 no.5
• /
• pp.10-21
• /
• 2006

For analyze of the bearing capacity, skin friction and settlements of pile on axial compressive loading, both Load transfer tests of pile and pile loading test in field have application to commonly before pile installing. A bearing capacity of pile was affected by the characteristics of surrounding ground of pile. Especially, that is very different because of evaluation of settlement due to each soil conditions of ground depths. The ground characteristics using evaluation of bearing capacity of pile through load transfer analysis depends on N values of SPT, and then a bearing capacity of pile installed soft ground and refilled area may be difficult to rational evaluation. An evaluation of bearing capacity on pile applied axial compressive loading was effected by strength of ground installed pile, unconfined compressive strength at pile tip, pile diameter, rough of excavated surface, confining pressure and deformation modules of rock etc and these are commonly including the unreliability due to slime occurred excavation works. Load transfer characteristics considered ground conditions take charge of load transfer of large diameter pile was investigated through case study applied load transfer tests. To these, matrix analytical technique of load transfer using finite differential equation developed and compared with the results of pile load test.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.13 no.6
• /
• pp.88-98
• /
• 2014

A moving mass on a skewed linear guideway model to analyze the friction-induced stick-slip behavior of ball-screw-driven slides is proposed. To describe the friction force, a friction coefficient function is modelled as a third-order polynomial of the relative velocity between the slide mass and a guideway. A nonlinear differential equation of motion is derived and an approximate solution is obtained using a perturbation method for the amplitudes and base frequencies of both pure-slip and stick-slip oscillations. The results are presented with time responses, phase plots, and amplitude plots, which are compared adequately with those obtained by Runge Kutta 4th-order numerical integration, as long as the difference between the static and kinematic friction coefficients is small. However, errors in the results by the approximate solution increase and are not negligible if the difference between the friction coefficients exceeds approximately 40% of the static friction coefficient.

• Journal of the Korean Physical Society
• /
• v.73 no.9
• /
• pp.1303-1309
• /
• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

• Water for future
• /
• v.24 no.4
• /
• pp.49-58
• /
• 1991

Flood routing in the Youngsan River was performed for the flood event of July, 1989 by two finite difference methods. The Saint Venant eq., a kind of hyperbolic partial differential equation is employed as governing equation and the explicit scheme (Leap Frog) and implicit scheme (Preissmann) are used to discretize the GE. As for the external boundary conditions, discharge and tidal elevation are upstream and downstream BC, respectively and estuary dam is included in internal BC. Lateral inflows and upstream discharges are the hourly results from storage function method, At Naju station, a Relatively upstream points in this river, the outputs are interpreted as good ones by comparing two numerical results of FDMs with the observed data and the calibrated results by storage function method. and two computational results are compared at the other sites, from middle stream and downstream points, and thus are considered reliable. Therefore, we can conclude from this research that these numerical models are adaptable in simulating and forecasting the flood in natural channels in Korea as well as existing hydrologic models. And the study about optimal gate control at the flood time is expected as further study using these models.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.4
• /
• pp.493-499
• /
• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.