• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.2
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• pp.165-174
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• 2007

Variable displacement type piston pump uses various controllers for controlling more than one state quantity like pressure, flow, power, and so on. These controllers need the mathematical model closely expressing dynamic behavior of pump for analyzing the stability of control systems which usually use various kinds of state variables. This paper derives the nonlinear mathematical model for variable displacement type piston pump. This model consists of two 1st oder differential equations by the continuity equations and one 2nd oder differential equation by the motion equation. To simplify the model we obtain the linear state variable model by differentiating the three nonlinear equations. And we verify this linearized model by comparison of simulation with experimentation and analyze the stability for the flow/pressure control. Finally this paper suggests the design compensation to ensure the stability of the systems.

• Journal of Digital Contents Society
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• v.18 no.1
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• pp.217-224
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• 2017

Recently, we have been continued effort that chaotic theory apply into love model which is an area of social science. To make the chaotic behaviors in the differential equation that represent as Romeo and Juliet, we apply an external force to the differential equation. However, this external force have disadvantage that cannot exactly represent for emotion of human. In this paper, to solve these advantage, we introduce triangular fuzzy membership function to provide the external force that can describe most similar status for action and word of human in the love model of Romeo and Juliet. Also, to confirm the chaotic behaviors in the love model of Romeo and Juliet with proposed fuzzy membership function, we use time series and phase plane.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.860-865
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• 2010

When a circuit breaker is opened, a large capacitance around the buses, the circuit breaker and the potential transformer (PT) might cause PT ferroresonance. During PT ferroresonance, the iron core repeats saturation and unsaturation even though the supplied voltage is a rated voltage. This paper describes an analytical analysis of PT ferroresonance in the transient-state. To analyze ferroresonance analytically, the iron core is modelled by a simplified two-segment core model in this paper. Thus, a nonlinear ordinary differential equation (ODE) for the flux linkage is changed into a linear ODE with constant coefficients, which enables an analytical analysis. In this simplified model, each state, which is either saturated or unsaturated state, corresponds to one of the three modes, i.e. overdamping, critical damping and underdamping. The flux linkage and the voltage in each state are obtained analytically by solving the linear ODE with constant coefficients. The proposed transient analysis is effective in the more understanding of ferroresonance and thus can be used to design a ferroresonance prevention or suppression circuit of a PT.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.11
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• pp.2098-2110
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• 1992

An analysis is presented for the combination resonance of a clamped circular plate, which occurs when the frequency of the excitation is near the combination of the natural frequencies, that is, when ohm.=2.0mega.／sub 1／+omega.／sub 2／. The internal resonance, Omega.／sub 3／=omega.／sub 1／+2.omega.／sub 2／, is considered and its influence on the response is studied. The clamped circular plate experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is used to obtain steady-state responses of the system. Results of numerical investigations show that the increase of the excitation amplitude can reduce the amplitudes of steady-state responses. We can not find this kind of results in linear systems.

• Smart Structures and Systems
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• v.24 no.3
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• pp.361-377
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• 2019

The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.99-105
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• 1994

In this study, the transverse and the torsional vibration analyses of a precision dynamic drive system with the magnetic coupling are accomplished. The force of the magnetic coupling is regarded as an equivalent transverse stiffness, which has a nonlinearity as a function of the gap and the eccentricity between a driver and a follower. Such an equivalent stiffness is calculated by and determined by the physical law and the calculated equivalent stiffness is modelled as the truss element. The form of the torque function transmitted through the magnetic coupling is a sinusoidal and such an equivalent angular stiffness, which represents the torque between a driver and a follower, is modelled as a nonlinear spring. The main spindle connected to a follower is assumed to a rigid body. And then finally we have the nonlinear partial differential equation with respect to the angular displacements. Through the procedure mentioned above, we accomplish the results of the torsional vibration analysis in a spindle system with the magnetic coupling.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.272-280
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• 2023

We study the numerical analysis for the Cahn-Hilliard (CH) equation using the decoupled projection (DP) method. The CH equation is a fourth order nonlinear partial differential equation that is hard to solve. Therefore, various of numerical schemes have been proposed to solve the CH equation. To verify the relation of each existing scheme for the CH equation, we consider the DP method for linear convex splitting schemes. We present the numerical experiments to demonstrate our analysis. Throughout this study, it is expected to construct a novel numerical scheme using the relation with existing numerical schemes.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.263-284
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• 2012

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.