• Structural Engineering and Mechanics
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• 제42권1호
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• pp.95-119
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• 2012

In this paper, forced vibration differential equations of motion of Euler-Bernoulli beams with different boundary conditions and dynamic loads are solved using differential transform method (DTM), analytical solutions. Then, the modal deflections of these beams are obtained. The calculated modal deflections using DTM are represented in tables and depicted in graphs and compared with the results of the analytical solutions where a very good agreement is observed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.253-266
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• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• Nuclear Engineering and Technology
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• 제49권8호
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• pp.1680-1688
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• 2017

In this study, analysis is performed on entropy generation during cilia transport of water based titanium dioxide nanoparticles in the presence of viscous dissipation. Moreover, thermal heat flux is considered at the surface of a channel with ciliated walls. Mathematical formulation is constructed in the form of nonlinear partial differential equations. Making use of suitable variables, the set of partial differential equations is reduced to coupled nonlinear ordinary differential equations. Closed form exact solutions are obtained for velocity, temperature, and pressure gradient. Graphical illustrations for emerging flow parameters, such as Hartmann number (Ha), Brinkmann number (Br), radiation parameter (Rn), and flow rate, have been prepared in order to capture the physical behavior of these parameters. The main goal (i.e., the minimizing of entropy generation) of the second law of thermodynamics can be achieved by decreasing the magnitude of Br, Ha and ${\Lambda}$ parameters.

• 대한수학회지
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• 제37권6호
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• pp.1043-1057
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• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.

• Korean Journal of Mathematics
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• 제3권1호
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• pp.21-28
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• 1995

• 대한수학회보
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• 제15권1호
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• pp.11-19
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• 1978

• Computers and Concrete
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• 제7권4호
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• 대한기계학회논문집A
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• 제25권11호
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• pp.1730-1736
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• 2001

A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modeling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are (derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, two weak forms are derived: one is for the chordwise motion and the other is fur the flptwise motion. The weak farms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviors of the natural frequencies are investigated for the variation of the rotating speed.

• Structural Engineering and Mechanics
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• 제25권5호
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• pp.501-518
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• 2007

In this work, a new approach is developed for dynamic analysis of a composite beam with an interply crack, based on finite element solution of partial differential equations with the use of the COMSOL Multiphysics package, allowing for fast and simple change of geometric characteristics of the delaminated area. The use of COMSOL Multiphysics package facilitates automatic mesh generation, which is needed if the problem has to be solved many times with different crack lengths. In the model, a physically impossible interpenetration of the crack faces is prevented by imposing a special constraint, leading to taking account of a force of contact interaction of the crack faces and to nonlinearity of the formulated boundary value problem. The model is based on the first order shear deformation theory, i.e., the longitudinal displacement is assumed to vary linearly through the beam's thickness. The shear deformation and rotary inertia terms are included into the formulation, to achieve better accuracy. Nonlinear partial differential equations of motion with boundary conditions are developed and written in the format acceptable by the COMSOL Multiphysics package. An example problem of a clamped-free beam with a piezoelectric actuator is considered, and its finite element solution is obtained. A noticeable difference of forced vibrations of the delaminated and undelaminated beams due to the contact interaction of the crack's faces is predicted by the developed model.

• 환경영향평가
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• 제10권4호
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• pp.319-326
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• 2001

This study is aimed at the development of a comprehensive web-based partial differential equation solver (WPDES) using multidimensional finite element method, which can be operated on the basis of world wide web. Overall issues of engineering and environmental information management and facility control could be implemented using this solver. This paper describes the development technique of the model, which is first part on development of partial differential equation solver. Conventional commercial general solver of computational fluid dynamics problems were investigated. All the relevant environmental models were analyzed to develop integrated environmental management system using WPDES. The governing equations and the parameters of investigated models were analyzed and integrated. Several numerical modules were invented for each partial differential term in partial differential equation of many related modeling problems. Each module was coded in the fashion of object oriented method, and was combined independently for the overall governing equation. WPDES has unique characteristic, which can analyze the problem through the suitable combination of modules without development of additional models for each environment problem with different governing equation, main variables, and parameters.