• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.1083-1088
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• 2004

This paper deals with the vibration and stability of a circular cylindrical shaft, modeled as a tapered thin-walled composite beam and spinning with constant angular speed about its longitudinal axis, and subjected to an axial compressive force. Hamilton's principle and the assumed mode method are employed to derive the governing equations of motion. The resulting eigenvalue problem is analyzed, and the stability boundaries are presented for selected taper ratios and axial compressive force combinations. Taking into account the directionality property of fiber reinforced composite materials, it is shown that for a shaft featuring flapwise-chordwise-bending coupling, a dramatic enhancement of both the vibration and stability behavior can be reached. It is found that by the structural tailoring and tapering, bending natural frequencies, stiffness and stability region can be significantly increased over those of uniform shafts made of the same material. In addition, the particular case of a classical beam with internal damping effect is also included.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.123-130
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• 2008

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.6 no.4
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• pp.291-295
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• 2005

In this paper, we propose a face recognition method using modified 2-D PCA. While the previous PCA method computes the covariance matrix by using one dimensional vectors, the 2-D PCA method computes the covariance matrix by directly using direct two dimensional image, and extracts the feature vectors by solving eigenvalue problem. The proposed method recognizes the faces by applying the modified 2-D PCA to face images and it gets linear transformation matrix using two covariance matrices. The experimental results indicates that the proposed method improved about $1\%$ and achieved more stability in recognition rate than conventional 2-D PCA.

• Proceedings of the KIEE Conference
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• summer
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• pp.156-158
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• 2004

Recently electrical industry has been rapidly restructured by deregulation in the developed countries. The voltage stability problem of a power system is associated with a rapid voltage drop due to heavy load and it occurs because of inadequate reactive power supply at some critical buses. More effective power system control means for line flow and bus voltage are required for applying FACTS. In this paper Jacobian method used to study on the voltage stability, The Jacobian method is to check the eigenvalue of the load flow Jacobian matrix. If the power system is unstable, one of the eigenvalues, at leasL has crossed the imaginary axis. This paper demonstrate enhancement of ATC by application of STATCOM at WSCC 9-bus system.

• Steel and Composite Structures
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• v.34 no.2
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• pp.241-260
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• 2020

This article presented a comprehensive model to study static buckling stability and associated mode-shapes of higher shear deformation theories of sandwich laminated composite beam under the compression of varying axial load function. Four higher order shear deformation beam theories are considered in formulation and analysis. So, the model can consider the influence of both thick and thin beams without needing to shear correction factor. The compression force can be described through axial direction by uniform constant, linear and parabolic distribution functions. The Hamilton's principle is exploited to derive equilibrium governing equations of unified sandwich laminated beams. The governing equilibrium differential equations are transformed to algebraic system of equations by using numerical differential quadrature method (DQM). The system of equations is solved as an eigenvalue problem to get critical buckling loads and their corresponding mode-shapes. The stability of DQM in determining of buckling loads of sandwich structure is performed. The validation studies are achieved and the obtained results are matched with those. Parametric studies are presented to figure out effects of in-plane load type, sandwich thickness, fiber orientation and boundary conditions on buckling loads and mode-shapes. The present model is important in designing process of aircraft, naval structural components, and naval structural when non-uniform in-plane compressive loading is dominated.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.

• Advances in nano research
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• v.7 no.4
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• pp.277-292
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• 2019

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.511-525
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• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• Steel and Composite Structures
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• v.33 no.2
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• pp.195-208
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• 2019

Based on a four-variable shear deformation shell theory, the free vibration analysis of functionally graded graphene platelet-reinforced composite (FGGPRC) doubly-curved shallow shells with different boundary conditions is investigated in this work. The doubly-curved shells are composed of multi nanocomposite layers that are reinforced with graphene platelets. The graphene platelets are uniformly distributed in each individual layer. While, the volume faction of the graphene is graded from layer to other in accordance with a novel distribution law. Based on the suggested distribution law, four types of FGGPRC doubly-curved shells are studied. The present shells are assumed to be rested on elastic foundations. The material properties of each layer are calculated using a micromechanical model. Four equations of motion are deduced utilizing Hamilton's principle and then converted to an eigenvalue problem employing an analytical method. The obtained results are checked by introducing some comparison examples. A detailed parametric investigation is performed to illustrate the influences of the distribution type of volume fraction, shell curvatures, elastic foundation stiffness and boundary conditions on the vibration of FGGPRC doubly-curved shells.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.5
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• pp.175-180
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• 2019

The optical characteristics and power transfers between guiding channels of blazed grating-assisted directional coupler (B-GADC) are evaluated in detail by using novel and rigorous modal transmission-line theory (MTLT) based on eigenvalue problem. To evaluate the coupling efficiency of B-GADC, the dispersion curves as a function of the grating period and wavelength are analyzed numerically for quasi-TE and quasi-TM modes. Furthermore, symmetric, sawtooth and asymmetric grating profiles are considered to know the effect of blazing characteristics on power transfer of GADC. The numerical results show that the grating period for minimum-gap condition to obtain maximum power transfer decreases gradually as the blazed structure changes from symmetric to asymmetric profile. On the other hand, the coupling length increases reversely.