• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1137-1152
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• 2005

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

• East Asian mathematical journal
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• v.35 no.1
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.116-119
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• 2007

In this study the unsteady aerodynamic analysis of a hovering helicopter rotor is performed. For the accurate flow field analysis Euler equations and the free wake method are coupled. The Euler equations are solved to find the pressure distribution around the rotor, and free wake method is used to give the boundary condition for the solution of Euler equations. Also, vortex strength and wake motion after the rotor are simulated by the free wake method. The accuracy of the present method is compared with the source sink model. The present method is applied to the hovering Caradonna-Tung rotor and compared with experimental results.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.9-17
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• 1996

This paper develops a sequential updating method of the Euler parameter generalized coordinates for the machine kinematics and dynamics, The Newton's method is slightly modified so as to utilize the Jacobian matrix with respect to the virtual rotation instead of this with repect to the Euler parameters. An intermediate variable is introduced and the modified Newton's method solves for the variable first. Relational equation of the intermediate variable is then solved for the Euler parameters. The solution process is carried out efficiently by symoblic inversion of the relational equation of the intermediate variable and the iteration equation of the Euler parameter normalization constraint. The proposed method is applied to a kinematic and dynamic analysis with the Generalized Coordinate Partitioning method. Covergence analysis is performed to guarantee the local convergence of the proposed method. To demonstrate the validity and practicalism of the proposed method, kinematic analysis of a motion base system and dynamic analysis of a vehicle are carried out.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.15-27
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• 2008

We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.

• Coupled systems mechanics
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• v.10 no.1
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.837-845
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• 1998

In this work, we consider Euler approxiamtion for one-dimensional jump-diffusion processes under Yamada-Watanabe type conditions on the coefficients which turns out to converge to the strong solution in uniform $L^1$-sense.

• Journal of Industrial Convergence
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• v.19 no.4
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• pp.23-28
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• 2021

This paper finds the regular pattern of n = [3, ∞] for Euler square game related with n = 6(6×6=36) thirty-six officer problem that is still unsolved problem. The solution of this problem is exists for n = [3, 10] without n = 6. Also, previous researchers finds the random assigned solution for specific number using computer programming. Therefore, the solution of n = [11, ∞] Euler squares are unsolved problem because of anything but easy. This paper attempts to find generalized patterns for domains that have been extended to n = [3, ∞], while existing studies have been limited to n = [3, 10]. This paper classify the n = [3, ∞] into n = odd, 4k even, 4k+2 even of three classes. Then we find the simple regular pattern solution for n = odd and 4k even(n/2 = even). But we can't find the regular pattern for 4k+2 even(n/2 = odd).

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.681-704
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• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.