• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.281-286
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• 2003

A Suspension system of a car is composed of dampers and springs. The dampers and springs usually have nonlinear characteristics. However, the nonlinear characteristics of the springs and dampers through analytical model cannot agree with the experimental results. Therefore, the nonlinearity of the suing and damper should be known from the experimental results. In this study, the methods of system identification for nonlinear dynamic system in time domain are discussed and the nonlinear parameter estimation lot experimental data of an EF-SONATA car was done. The results show that a cubic and a coupled term should be considered to model the suspension system.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.9
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• pp.1104-1109
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• 1992

A mathematical model of cancerous system based on immunological surveillance has been proposed by Lee. The model involves a system of 12 coupled nonlinear differential equations due to cellular kinetics and each of them can be modeled bilinearly. This paper discusses only the properties of solutions to the nonlinear differential equations and identification.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.437-450
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• 2023

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩^*_λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• 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 KSR Conference
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• 2010.06a
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• pp.1478-1485
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• 2010

In this paper, the nonlinear dynamic response of Vehicle-Bridge interaction with the coupled equations of motion including nonlinear Hertzian contact is presented. The moving train model is chosen to have 10 degrees of freedom (DOF). The bridge is modeled as 2D Euler-Bernoulli beam element with 4 DOF for each element, two for rotations and another two for translations. The nonlinear Hertzian contact is used to simulate the interaction between vehicle and bridge. Base on the relationship of wheel displacement of the vehicle and the vertical displacement of the bridge in Hertzian contact, the coupled equations of motion of the whole system is derived. The convenient formulation was encoded into a computer program. The contact forces, contact area and stress of the rail surface were also computed. The accuracy and efficiency of the proposed program are verified and compared with exact analytical solution and other previous studies. Various numerical examples and parametric studies have demonstrated the versatility and applicability of the proposed program.

• Journal of Photoscience
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• v.10 no.2
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• pp.203-208
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• 2003

Two coupled molecules were successfully synthesized by condensation of amine-donor-substituted barbituric acid derivativies as nonlinear optical chromophores. A flexible spacer of the alkyl chain with different lengths of carbon chains (5 and 6 carbons) was introduced between two chromophores, which prevented crystallization and aggregation of molecules. Two coupled molecules (B-Cn-B, n=5, 6) had glass-transition temperatures on a second heating around 81 and 76$^{\circ}C$ without melting points, respectively. To explore the linear optical properties, thin-films were prepared and examined by a photometry method using Nd:YVO$_4$ CW laser. Also, microscopic and macroscopic nonlinear optical properties were measured by Hyper-Rayleigh Scattering (HRS) and the Maker Fringes method using Nd:YAG ps pulse laser, respectively. In spite of the moderate hyperpolarizabilities of coupled molecules, the second order NLO coefficient (d$\_$33/) was larger than the conventional Disperse Red 1 doped PMMA polymeric system.

• Journal of KSNVE
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• v.8 no.6
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• pp.1144-1149
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• 1998

A two degree-of-freedom model of suspended cables is studied for forced resonant response. The method of averaging is used to obtain first-order approximations to the response of the system. A bifurcation analysis of the averaged system is performed in the case of 2-to-1 internal resonance. Nonlinear coupled-mode motions are found to bifurcate from single-mode responses and further bifurcate to limit cycle motions via Hopf bifurcations. The limit cycle solutions undergo period doubling bifurcations to chaos.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.513-527
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• 2011

The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.

• Coupled systems mechanics
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• v.1 no.3
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• pp.247-268
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• 2012

A finite element model is developed for dynamic response prediction of floating offshore wind turbine systems considering coupling of wind turbine, floater and mooring system. The model employs Morison's equation with Srinivasan's model for hydrodynamic force and a non-hydrostatic model for restoring force. It is observed that for estimation of restoring force of a small floater, simple hydrostatic model underestimates the heave response after the resonance peak, while non-hydrostatic model shows good agreement with experiment. The developed model is used to discuss influence of heave plates and modeling of mooring system on floater response. Heave plates are found to influence heave response by shifting the resonance peak to longer period, while response after resonance is unaffected. The applicability of simplified linear modeling of mooring system is investigated using nonlinear model for Catenary and Tension Legged mooring. The linear model is found to provide good agreement with nonlinear model for Tension Leg mooring while it overestimates the surge response for Catenary mooring system. Floater response characteristics under different wave directions for the two types of mooring system are similar in all six modes but heave, pitch and roll amplitudes is negligible in tension leg due to high restraint. The reduced amplitude shall lead to reduction in wind turbine loads.