• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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• pp.109-116
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• 1998

The method of vibration analysis used is the one developed by the senior author. He developed and reported, in 1974, a simple but exact method of calculating the natural frequency of beam and tower structures with irregular cross-sections and attached mass/masses. Since 1989, this method has been extended to two-dimensional problems with several types of given conditions and has been reported at several international conferences. This method uses the deflection influence surfaces. The finite difference method is used for this purpose, in this paper. In order to reduce the pivotal points required, the three simultaneous partial differential equations of equilibrium with three dependent variables, w, M$_{x}$, and $M_{y}$, are used instead of the one forth order partial differential equation. By neglecting the M$_{x}$ terms, the size of the matrices needed to solve the resulting linear equations are reduced to two thirds of the "non-modified" equations.tions.

• Journal of Magnetics
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• 제21권1호
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• pp.153-158
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• 2016

This paper aims to discuss the Non Darcy boundary layer flow of non-conducting viscous fluid with magnetic ferroparticles over a permeable linearly stretching surface with ohmic dissipation and mixed convective heat transfer. A magnetic dipole is applied "a" distance below the surface of stretching sheet. The governing equations are modeled. Similarity transformation is used to convert the system of partial differential equations to a system of non-linear but ordinary differential equations. The ODEs are solved numerically. The effects of sundry parameters on the flow properties like velocity, pressure, skin-friction coefficient and Nusselt number are presented. It is deduced the frictional resistance of Lorentz force decreases with stronger electric field and the trend reverses for temperature. Skin friction coefficient increase with increase in ferromagnetic interaction parameter. Whereas, Nusselt number decrease.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.459-475
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• 2005

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

• 대한전기학회논문지
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• 제39권7호
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• pp.740-748
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• 1990

In this paper, we consider the problem of parameter estimation, i.e., definding the internal structure of a linear distribution parameter system from its input/output data. First, a linear partial differential equation describing the system is double-integrated with respect to two variables and then transformed into an integral equation. Next the Walsh Operation Matrix for Walsh function and their integration are introduced to transform the integral equation into algebraic simultaneous equations. Finally, we develop an algorithm to estimate the parameters of the linear distributed parameter system from the simple linear algebraic simultaneous equations. It is also shown that our algorithm could be effective in real time data processing since it uses the Fast Walsh Transform.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.319-330
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• 2020

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

• Structural Engineering and Mechanics
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• 제34권4호
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• 대한수학회지
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• 제37권4호
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• pp.593-611
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• 2000

For linear time-varying control systems with constrained control described by both differential and discrete-time equations in Banach spaces was give necessary and sufficient conditions for exact global null-controllability. We then show that for such systems, complete stabilizability implies exact null-controllability.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.45-60
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• 2017

This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.