• Advances in aircraft and spacecraft science
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• v.7 no.3
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• pp.215-228
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• 2020

As is shown in the paper, the Koltunov-Rzhanitsyn singular kernel of heredity (when constructing mathematical models of the dynamics problem of the hereditary theory of viscoelasticity) adequately describes real mechanical processes, best approximates experimental data for a long period of time. A mathematical model of the problem of the flutter of viscoelastic plates moving in a gas with a high supersonic velocity is given. Using the Bubnov-Galerkin method, discrete models of the problem of the flatter of viscoelastic plates flowed over by supersonic gas flow are obtained. A numerical method is developed to solve nonlinear integro-differential equations (IDE) for the problem of the hereditary theory of viscoelasticity with weakly singular kernels. A general computational algorithm and a system of application programs have been developed, which allow one to investigate the nonlinear dynamic problems of the hereditary theory of viscoelasticity with weakly singular kernels. On the basis of the proposed numerical method and algorithm, nonlinear problems of the flutter of viscoelastic plates flowed over in a gas flow at an arbitrary angle are investigated. In a wide range of changes in various parameters of the plate, the critical velocity of the flutter is determined. It is shown that the singularity parameter α affects not only the oscillations of viscoelastic systems, but the critical velocity of the flutter as well.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.16-19
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• 1996

The objective of this paper is to present a new adaptive nonlinear compensation method, which is based upon the Pth-order inverse theory and can be implemented in a systematic way, for weakly nonlinear systems that can be modeled by a Volterra series. In particular, employment of the proposed approach for the linearization of a given nonlinear system leads to the effective elimination of (up to a required order) nonlinearities in the overall system output. To demonstrate the feasibility of the proposed method, simulation results using a satellite communication system model are also provided.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5B
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• pp.539-549
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• 2006

The performance of a pontoon-type floating breakwater (FB) is investigated numerically with the use of a second-order time domain model. The model has been developed based on potential theory, perturbation theory and boundary element method. This study is focused on the effects of weakly nonlinear wave on the hydrodynamic characteristics of the FB. Hydrodynamic forces, motion responses, surface elevation, and wave transmission coefficient around the floating breakwater are evaluated for various wave and geometric parameters. It is shown that the second-order wave component is of significant importance in calculating magnitudes of the hydrodynamic forces, mooring forces and the maximum response of a structure. The weak non-linearity of incident waves, however, can have little influence on the efficiency of the FB. From numerical simulations, the ratio of draft and depth, the relationship of wave number and width are presented for providing an effective means of reducing wave energy.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• Journal of Energy Engineering
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• v.10 no.3
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• pp.266-271
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• 2001

Buoyancy-driven natural convection is analysed by employing a linear stability theory in hori-zontal porous media with net through flow. Darcy's law is used to model the flow characteristics in porous media. Bated on the results of linear stability analysis, a heat transfer correlation was obtained by employing weakly nonlinear analysis. As the net through flow increases, the system becomes more stable and the effect of the Darcy-Rayleigh number on the Nusselt number decreases.

• Ocean Systems Engineering
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• v.8 no.4
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• pp.381-407
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• 2018

This paper presents a hybrid numerical approach, which combines a two-phase Navier-Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain near the structure, where the viscous and turbulent effects are significant, and is solved by OpenFOAM/InterDyMFoam which utilising the finite volume method (FVM) with a Volume of Fluid (VOF) for the phase identification. The latter covers the rest of the domain, where the fluid may be considered as incompressible, inviscid and irrotational, and solved by using the Quasi Arbitrary Lagrangian-Eulerian finite element method (QALE-FEM). These two models are weakly coupled using a zonal (spatially hierarchical) approach. Considering the inconsistence of the solutions at the boundaries between two different sub-domains governed by two fundamentally different models, a relaxation (transitional) zone is introduced, where the velocity, pressure and surface elevations are taken as the weighted summation of the solutions by two models. In order to tackle the challenges associated and maximise the computational efficiency, further developments of the QALE-FEM have been made. These include the derivation of an arbitrary Lagrangian-Eulerian FNPT and application of a robust gradient calculation scheme for estimating the velocity. The present hybrid model is applied to the numerical simulation of a fixed horizontal cylinder subjected to a unidirectional wave with or without following current. The convergence property, the optimisation of the relaxation zone, the accuracy and the computational efficiency are discussed. Although the idea of the weakly coupling using the zonal approach is not new, the present hybrid model is the first one to couple the QALE-FEM with OpenFOAM solver and/or to be applied to numerical simulate the wave-structure interaction with presence of current.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.3
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• pp.187-197
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• 2015

This study aims the development of a semi-analytic method for the parametric roll of large containerships advancing in longitudinal waves. A 1.5 Degree-of-Freedom(DOF) model is proposed to account the change of transverse stability induced by wave elevations and vertical motions (heave and pitch). By approximating the nonlinearity of restoring moment at large heel angles, the magnitude of roll amplitude is predicted as well as susceptibility check for parametric roll occurrence. In order to increase the accuracy of the prediction, the relationship between righting arm(GZ) and metacentric height(GM) is examined in the presence of incident waves, and then a new formula is proposed. Based on the linear approximation of the mean and first harmonic component of GM, the equation of parametric roll in irregular wave excitations is introduced, and the computational results of the proposed model are validated by comparing those of weakly nonlinear simulation based on an impulse-response-function method combined with strip theory. The present semi-analytic doesn’ t require heavy computational effort, so that it is very efficient particularly when numerous sea conditions for the analysis of parametric roll should be considered.