• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Journal of the Korean Society for Railway
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• v.5 no.1
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• pp.40-47
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• 2002

In this study, and analytical method for ride sensitivity analysis of a train with non-linear suspension elements are proposed. Non-linear characteristics of springs and dampers for primary and secondary suspensions of a train are parameterized using polynomial interpolation. Vertical dynamic model of a three-body train running on straight rail with the predetermined roughness expressed in terms of spectral density function is set up and its equations of motion for ride analysis are derived. Using the direct differentiation method, sensitivity equations of the vertical dynamic model with respect to design parameters associated with non-linearity of suspensions are obtained. Based on the sensitivity analysis, improvement of ride is achieved by varying appropriate suspension parameters.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.1
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• pp.64-71
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• 2015

This paper deals with analysis of armature reaction magnetic field of linear generator with three phases coreless/cored type concentrated winding. On the basis of a magnetic vector potential and Maxwell's equations, governing equations to predict armature reaction field are derived, and current density modeling is also performed analytically by using the Fourier series expansion. The analytical method used in this paper is confirmed by comparing with finite element analysis results.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.121-126
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• 1998

A numerical optimization procedure is developed to find the inlet velocity profile that yields the most uniform epitaxial layer in a vertical MOCVD reactor. It involves the solution of fully elliptic equations of motion, temperature, and concentration; the finite volume method based on SIMPLE algorithm has been adopted to solve the Navier-Stokes equations. The overall optimization process is highly nonlinear and has been efficiently treated by the sequential linear programming technique that breaks the non-linear problem into a series of linear ones. The optimal profile approximated by a 6th-degree Chebyshev polynomial is very successful in reducing the spatial non-uniformity of the growth rate. The optimization is particularly effective to the high Reynolds number flow. It is also found that a properly constructed inlet velocity profile can suppress the buoyancy driven secondary flow and improve the growth-rate uniformity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.574-581
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• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Steel and Composite Structures
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• v.25 no.4
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• pp.497-503
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• 2017

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.432-435
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• 1995

In this paper a new approach to obtain the solution of the linear-quadratic Gaussian control problem for singularly perturbed discrete-time stochastic systems is proposed. The alogorithm proposed is based on exploring the previous results that the exact solution of the global discrete algebraic Riccati equations is found in terms of the reduced-order pure-slow and pure-fast nonsymmetric continuous-time algebraic Riccati equations and, in addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.689-696
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• 2006

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of taper types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both clamped ends and both hinged ends are considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are investigated extensively. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.7
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• pp.1125-1130
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• 2001

Dynamic behaviors of an automatic dynamic balancer are analyzed by a theoretical approach. Using the polar coordinates, the non-linear equations of motion for an automatic dynamic balancer equipped in a rotor with the bending flexibility are derived from Lagrange equation. Based on the non-linear equation, the stability analysis is performed by using the perturbation method. The stability results are verified by computing dynamic response. The time responses are computed from the non-linear equations by using a time integration method. We also investigate the effect of the bending flexibility on the dynamics of the automatic dynamic balancer.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.845-862
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• 2010

In a recent paper, M.A. Noor et al. (Hindawi publishing corporation, Mathematical Problems in Engineering, Volume 2008, Article ID 696734, 11 pages, doi:10.1155/2008/696734) proposed the variational homotopy perturbation method (VHPM) for solving higher dimentional initial boundary value problems. In this paper, we consider the proposed method for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The results reveal that the proposed method is very effective and simple and can be applied for other linear and nonlinear problems in mathematical.