• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.3031-3040
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• 1995

Two-dimensional incompressible Navier-Stokes equations have been solved by the node-centered finite volume method with the unstructured triangular meshes. The pressure-velocity coupling is handled by the artificial compressibility algorithm due to its computational efficiency associated with the hyperbolic nature of the resulting equations. The convective fluxes are obtained by the Roe's flux difference splitting scheme using edge-based connectivities and higher-order differences are achieved by a reconstruction procedure. The time integration is based on an explicit four-stage Runge-Kutta scheme. Numerical procedures with local time stepping and implicit residual smoothing have been implemented to accelerate the convergence for the steady-state solutions. Comparisons with experimental data and other numerical results have proven accuracy and efficiency of the present unstructured approach.

• Steel and Composite Structures
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• v.24 no.6
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• pp.671-677
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• 2017

In this paper, two powerful analytical methods called Variational Approach (VA) and Hamiltonian Approach (HA) are used to solve high nonlinear non-Natural vibration problems. The presented approaches are works well for the whole range of amplitude of the oscillator. The first iteration of the approaches leads us to high accurate solution. Numerical results are also presented by using Runge-Kutta's [RK] algorithm. The full comparison between the presented approaches and the numerical ones are shown in figures. The effects of important parameters on the response of nonlinear behavior of the systems are studied completely. Finally, the results show that the Variational Approach and Hamiltonian approach are strong enough to prepare easy analytical solutions.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

• Computational Structural Engineering
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• v.7 no.3
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• pp.95-103
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• 1994

The safety related components in the nuclear power plant should be designed to withstand the seismic load. Among these components the integrity of reactor internals under earthquake load is important in stand points of safety and economics, because these are classified to Seismic Class I components. So far the modelling methods of reactor internals have been investigated by many authors. In this paper, the dynamic behaviour of reactor internals of Yong Gwang 1&2 nuclear power plants under SSE(Safe Shutdown Earthquake) load is analyzed by using of the simpled Global Beam Model. For this, as a first step, the characteristic analysis of reactor internal components are performed by using of the finite element code ANSYS. And the Global Beam Model for reactor internals which includes beam elements, nonlinear impact springs which have gaps in upper and lower positions, and hydrodynamical couplings which simulate the fluid-filled cylinders of reactor vessel and core barrel structures is established. And for the exciting external force the response spectrum which is applied to reactor support is converted to the time history input. With this excitation and the model the dynamic behaviour of reactor internals is obtained. As the results, the structural integrity of reactor internal components under seismic excitation is verified and the input for the detailed duel assembly series model could be obtained. And the simplicity and effectiveness of Global Beam Model and the economics of the explicit Runge-Kutta-Gills algorithm in impact problem of high frequency interface components are confirmed.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.3
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• pp.107-116
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• 1990

The liquid sloshing in an elastic tank is a fluid-structure interaction problem. It requires nonlinear analysis to solve the complicated physics involved in the large interaction of fluid-structure, the variation of dynamic characteristics of structure due to hydrodynamic loading, and the distorsion of fluid flow due to structural vibration. In this paper a Lagrangian FEM is introduced to analyze the liquid sloshing in an elastic tank assuming that the elastic wall is one degree of freedom rigid wall. Numerical integration is performed using an implicit-explicit algorithm, which is formed by mixing the predictor-corrector method and the Runge-Kutta 4th order method. The influence of dynamic characteristics of the sloshing tank on the fluid flow is discussed. The numerical method is also applied for the simulation of the wall generated wave in the tank.

• Journal of KSNVE
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• v.11 no.2
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• pp.336-345
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• 2001

This research presents a nonlinear model to analyze the ball bearing nitration due to the waviness in a rigid rotor supported by multi-row ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by the multi-row ball bearings with waviness. It also characterizes the nitration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing. and the sideband frequencies resulting from the waviness interaction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Journal of Soil and Groundwater Environment
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• v.13 no.6
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• pp.50-61
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• 2008

In this study, new integrated particle tracking algorithm was developed to reduce the inherent problem of Eulerian- Lagrangian method, or adverse effect of particle tracking error on mass balance error. The new integrated particle tracking algorithm includes numerical method, semi-analytical method, and analytical method which consider both temporal and spatial changes of velocity field during time step. Detail of mathematical derivations is well illustrated and four examples are made to verify through the comparison of the new integrated particle tracking with analytical solution or Runge-Kutta method. Additionally, It was shown that the there is better superiority of the new integrated particle tracking algorithm over other existing particle tracking method such as Lu's method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2636-2646
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• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.2
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• pp.140-145
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• 2018

This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.