• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1751-1758
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• 1994

A new set of governing equations is derived for the dynamic analysis of the Free-Piston Stirling Engines(EPSE). Equations from the ideal adiabatic model for the thermodynamic analysis of the working fluid are incoporated with the equations of motion for the moving masses of the system, resulting in a set of nonlinear differential equations. The coupled set of equations are numerically integrated with proper intial conditions to obtain a steady state response of the engine. The proposed method is compared with the conventional method of analyzing EPSE based mainly on the ideal isothermal model. The results clearly shows the limitationsl of the conventional methods and the relative advantages of the method proposed in the present study.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.547-551
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• 1995

We analyze the nonlinearity of chiral media and coupled-mode theory of chiral multilayers. In first topic, second order nonlinear coupled equations are constructed and a phase matchine method is suggested. This approach can be developed to higher order nonlinearity and electric-field-induced second harmonic generation. In second topic, coupled mode equation in chiral multilayers is constructed, and solved for both codirectional coupling and contradirectional coupling. There is a previous formulation about chiral mutilayers[1] with 4$\times$4 matrix but it did not give detail results, so this approach will be compared with that.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.273-288
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• 2021

We proposed to give some new 𝜓-coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.

• Journal of Ocean Engineering and Technology
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• v.6 no.2
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• pp.41-45
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• 1992

In this paper an application technique of moment equation method to solution of nonlinear rolling equation of motion of ships is investigated. The exciting moment in the equation of rolling motion of ships is described as non-white noise. This non-white exciting moment is generated through use of a shaping filter. These coupled equations are used to generate moment equations. The nonstationary responses of the nonlinear system are obtained. The results are compared with those of a linear system.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.635-654
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• 2014

We consider the Cauchy problem for a Keller-Segel-fluid model with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.

• Wind and Structures
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• v.20 no.2
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• pp.249-274
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• 2015

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.31-34
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• 2002

An efficient implicit multigrid method is presented for the Navier-Stokes and $k-{\omega}$ turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. The eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.

• Journal of KSNVE
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• v.10 no.5
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• pp.838-842
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflection. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e. the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized nonlinear equations, the time responses are investigated by using the generalized-$\alpha$ method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.304-311
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• 2001

This research numerically analyzes the dynamic characteristics of a coupled journal and thrust hydrodynamic bearing due to its groove location which has the static load due to the weight of a rotor in the axial direction and the dynamic load due to its mass unbalance in the radial direction. The Reynolds equation is transformed to solve a plain member rotating type of journal bearing(PMRJ), a grooved member rotating type of journal bearing (GMRJ), a plain member rotating type of thrust bearing (PMRT) and a grooved member rotating type of thrust bearing (GMRT). FEM is used to solve the Reynolds equations in order to calculate the pressure distribution in a fluid film. Reaction forces and friction torque are obtained by integrating the pressure and shear stress along the fluid film, respectively. Dynamic behaviors, such as whirl radius or floating height of a rotor, are determined by solving its nonlinear equations of motion with the Runge-Kutta method. This research shows that the groove location affects the pressure distribution in the fluid film and consequently the dynamic performance of a HDD spindle system.

• Coupled systems mechanics
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• v.5 no.4
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• pp.285-304
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• 2016

The effects of large rotations and p-delta on the dynamic response of a structure subjected to seismic loading and local uplift of its foundation were analyzed in this work. The structure was modeled by an equivalent flexible mat mounted on a rigid foundation that is supported either by a Winkler soil type or a rigid soil. The equations of motion of the system were derived by taking into account the equilibrium of the coupled foundation-mat system where the structure was idealized as a single-degree-of-freedom. The obtained nonlinear coupled system of ordinary differential equations was integrated by using an adequate numerical scheme. A parametric study was performed then in order to evaluate the maximum response of the system as function of the intensity of the earthquake, the slenderness of the structure, the ratio of the mass of the foundation to the mass of the structure. Three cases were considered: (i) local uplift of foundation under large rotation with the p-delta effect, (ii) local uplift of foundation under large rotation without including the p-delta effect, (iii) local uplift of foundation under small rotation. It was found that, in the considered ranges of parameters and for moderate earthquakes, assuming small rotation of foundation under seismic loading can yield more adverse structural response, while the p-delta effect has almost no effect.