• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.221-228
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• 1997

The main purpose of this paper is to determine the dynamic optimal shapes of simple beam-columns with the constant volume. The parabolic function is chosen as the variable equation for the depth of regular polygon cross-section. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the simple beam-columns are analysed and the numerical results of this study are shown in tables and figures.

• Ocean Systems Engineering
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• v.6 no.4
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• pp.363-375
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• 2016

Large numbers of submarine pipelines are laid as the world now is attaching great importance to offshore oil exploitation. Free spanning of submarine pipelines may be caused by seabed unevenness, change of topology, artificial supports, etc. By combining Iwan's wake oscillator model with the differential equation which describes the vibration behavior of free-span submarine pipelines, the pipe-fluid coupling equation is developed and solved in order to study the effect of both internal and external fluid on the vibration behavior of free-span submarine pipelines. Through generalized integral transform technique (GITT), the governing equation describing the transverse displacement is transformed into a system of second-order ordinary differential equations (ODEs) in temporal variable, eliminating the spatial variable. The MATHEMATICA built-in function NDSolve is then used to numerically solve the transformed ODE system. The good convergence of the eigenfunction expansions proved that this method is applicable for predicting the dynamic response of free-span pipelines subjected to both internal flow and external current.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.295-318
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• 2018

This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).

• Coupled systems mechanics
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• v.9 no.1
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• pp.77-89
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• 2020

This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.705-714
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• 2012

In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any ${\lambda}$ < ${\lambda}^*$ and no solution for any ${\lambda}$ > ${\lambda}^*$. We show that when ${\lambda}$ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.

• 한국연소학회:학술대회논문집
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• 2006.04a
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• pp.167-171
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• 2006

The previous models for thermal behavior in the melting furnace were deterministic, composed of such a form that if the initial input conditions are determined, the results would have been come out by using the basic heat equilibrium equations. But making the experiment by trusting the analysis results, the melted slag is fortuitously set often, because temperature variation of the melted slag in the reaction process is not point function but path function. So in this study, a transient model was developed and verified by comparing with the experimental results.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.195-205
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• 2003

For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional $\rho$-Laplaclan: ($\Phi$$_{\rho}$(y'))'(t)+m(t)f(t, $y^{t}$ )=0 for t$\in$[0,1], y(t)=η(t) for t$\in$[-$\sigma$,0], y'(t)=ξ(t) for t$\in$[1,d], suitable conditions are imposed on f(t, $y^{t}$ ) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2252-2254
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• 2001

This paper proposes a algebraic parameter determination of MRAC (Model Reference Adaptive Control) controller using block Pulse functions and block Pulse function's differential operation. Generally, adaption is performed by solving differential equations which describe adaptive low for updating controller parameter. The proposes algorithm transforms differential equations into algebraic equation, which can be solved much more easily in a recursive manner. We believe that proposes methods are very attractive and proper for parameter estimation of MRAC controller on account of its simplicity and computational convergence.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.139-148
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• 2024

The purpose of this research is to investigate sufficient conditions for the existence of limit cycles of the fifth-order differential equation x⁽⁵⁾ + (p² + q²)$_{x}^{...}$ + p²q²$_{x}^{.}$ = εF(t, x, $_{x}^{.}$, $_{x}^{..}$, $_{x}^{...}$, $_{x}^{....}$), where p, q are rational numbers different from 0, p ≠ ±q, ε is a small real parameter, and F is a 2kπ-periodic function in the variable t. Also, we provide some applications.