• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.23-38
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• 2004

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in $R^d$. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in $W^{1,p}(\Omega)\;and\;L_p(\Omega)$, for $2\;{\leq}p\;<\;{\infty}$.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.105-114
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• 2005

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.535-550
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• 2005

The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.331-349
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• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.433-456
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• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.440-445
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• 1992

The major purpose here is to estimate the drying time required in the fish-drying process employed. The basic element of the prediction of the drying time is the model or the equation, which governs the change in weight. By an intuitive consideration on the mechanism of dehydration, a mathematical model of the fish-drying process is built, which is described by a system of linear differential equations. Further, a modified system of linear differential equations for a model of drying is also proposed for more accurate estimation. The parameter estimation of this system of equations provides the prediction of necessary drying time.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.101-110
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• 2000

This paper introduces the equivalent frequency response method(EFRM) into runoff analysis. This EFRM originally had been developed to analyze dynamic behavior of nonlinear elements such as threshold and saturation in control engineering. Many runoff models are described by nonlinear ordinary of partial differential equations This paper presents that these nonlinear differential equations can be converted into semi-linear ones based on EFRM. The word of "a semi-linear equation" means that the coefficients of derived equations depend on average rainfall.