• The Journal of the Korea Contents Association
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• v.3 no.3
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• pp.103-109
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• 2003

Functional equations are useful in the expermental science because they play very important to formulate mathematical moods in general terms, through some not very restrictive equations, without postulating the forms of such functions. In this paper n solve one of a generalized quadratic functional equation (equation omitted) and prove the stability of this equation.

• The KSFM Journal of Fluid Machinery
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• v.19 no.5
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• pp.12-19
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• 2016

In present study, a parametric study of a centrifugal compressor with inlet treatment has been performed numerically using three-dimensional Reynolds-averaged Navier-Stokes equations. The shear stress transport turbulence model was used for analysis of turbulence. The finite volume method and unstructured grid system were used for the numerical solution. Tested parameters were related to the geometry of the inlet duct. It was found that the application of circumferentially distributed holes in the inlet duct improves operational stability of the compressor compared to that with conventional inlet duct.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.904-910
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• 2001

Static and oscillatory loss of stability of composite pipes conveying fluid is investigated. The theory of thin walled beams is applied and transverse shear, rotary inertia, primary and secondary warping effects are incorporated. The governing equations and the associated boundary conditions are derived through Hamilton's variational principle. The governing equations and the associated boundary conditions are transferred to eigenvalues problem which provides the information about the dynamic characteristics of the system. Numerical analysis is performed by using extended Gelerkin method. Critical velocity of fluid is investigated by increasing fiber angle and mass ratio of fluid to pipe including fluid.

• Steel and Composite Structures
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• v.3 no.5
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• pp.307-320
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• 2003

This paper presents an efficient approach to the determination of the buckling loads of down-aisle, spliced, unbraced, pallet rack structures subjected to vertical and horizontal loads. A pallet rack structures is analysed by considering the stability equations of an equivalent free-sway column. The effects of semi-rigid beam-to-upright, splice-to-upright and base-plate-to-upright connections are fully incorporated into the analysis. Each section of upright between successive beam levels in the pallet rack is considered to be a single column element with two rotational degrees of freedom. A computer algebra package was used to determine modified stability equations for column elements containing splices. The influence of the position of splices in a pallet rack is clearly demonstrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.647-651
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• 2000

This paper deals with the dynamic stability of a vertical cantilevered pipe conveying fluid and having two attached masses. Some valves or other mechanical components in pipe systems can be regarded as attached lumped masses. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to discretize the equations of small motion of the pipe. Effects of attached masses on the dynamic stability of a vertical cantilevered pipe conveying fluid are investigated for various locations and magnitudes of the attached lumped masses.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.7
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• pp.1125-1130
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• 2001

Dynamic behaviors of an automatic dynamic balancer are analyzed by a theoretical approach. Using the polar coordinates, the non-linear equations of motion for an automatic dynamic balancer equipped in a rotor with the bending flexibility are derived from Lagrange equation. Based on the non-linear equation, the stability analysis is performed by using the perturbation method. The stability results are verified by computing dynamic response. The time responses are computed from the non-linear equations by using a time integration method. We also investigate the effect of the bending flexibility on the dynamics of the automatic dynamic balancer.

• Journal of Mechanical Science and Technology
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• v.18 no.12
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• pp.2148-2157
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• 2004

The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton's principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation parameters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.961-966
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• 2008

In this paper, the purpose is to investigate the stability and variation of natural frequency of a Timoshenko cantilever beam subjected to Subtangential follower force and tip mass. In addition, an analysis of the flutter instability(flutter critical follower force) of a cantilever beam as slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is derived via Hamilton;s principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. Finally, the influence of the slenderness ratio and tip mass on the critical follower force and the natural frequency of a Timoshenko beam are investigated.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.