• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1192-1201
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• 2009

Analysis of the vibration characteristic for cylindrical shell is more complex than plates since the coupling effects are considered on three dimensions. Based on Love's equation, spectral finite element method(SFEM) is introduced to predict frequency response function of finite circular cylindrical shell in the air with simply supported - free boundary condition without simplifying the equation of motion. And for the radiated noise analysis of cylindrical shell, indirect boundary element method(BEM) is applied using out-of-plane displacements as an input from structural vibration analysis. Comparisons of the structural vibration results by the spectral finite element method and commercial code, NASTRAN(FEM based) are carried out. Likewise, for verification of radiated noise analysis results, commercial code, SYSNOISE(BEM based) are used.

• Journal of Power System Engineering
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• v.9 no.4
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• pp.71-76
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• 2005

Marine structures are often in contact with inner or outer fluid as stern, ballast and oil tanks. The effect of interaction between fluid and structure has to be taken into consideration when we estimate the dynamic response of the structure appropriately. Fatigue damages can also be sometimes observed in these tanks which seem to be caused by resonance. Thin walled tank structures in ships which are in contact with water and located near engine or propeller where vibration characteristics are strongly affected by the added mass of containing water. Therefore it is essentially important to estimate the added mass effect to predict vibration characteristics of tank structures. But it is difficult to estimate exactly the magnitude of the added mass because this is a fluid-structure interaction problem and is affected by the free surface, vibration modes of structural panels and the depth of water. I have developed a numerical tool of vibration analysis of 3-dimensional tank structure using finite elements for plates and boundary elements for fluid region. In the present study, the effect of added mass of containing water, the effect of structural constraint between panels on the vibration characteristics are investigated numerically and discussed. Especially a natural frequencies by the fluid interaction between 2 panels and a breath mode of the water tank are focused on.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.526-529
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• 2004

Arches are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. This study deals with the free vibration of arbitrary shaped arches. In order to obtain the exactly arch shape, which surveyed (x, y) of neutral axis of arbitrary shaped arches are compared to various shape of arch: circular, parabolic, sinusoidal, elliptic, spiral and cartenary. The differential equations governing free vibrations of arches are merely adopted in the open literature rather than deriving the equations in this study. The Taylor series method is used as the numerical differential scheme. The Runge-Kutta method and the Regula-Falsi method, respectively, are used to integrate the governing differential equations and to compute the natural frequencies It is expected that results obtained herein can be practically utilized in the fields of vibration control.

• Special Issue of the Society of Naval Architects of Korea
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• 2015.09a
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• pp.56-62
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• 2015

In ship structure, many parts are in contact with inner or outer fluid as stern, ballast and oil tanks. Fatigue damages are sometimes observed in these tanks which seem to be caused by resonance with exciting force of engine and propeller. Vibration characteristics of these tanks in contact with fluid are significantly affected by fluid coupling effect. Therefore it is important to exactly predict vibration characteristics of tank structure. In order to estimate the vibration characteristics, the fluid-structure interaction(FSI) problem should be solved precisely. But it is difficult to estimate exactly the magnitude of the fluid coupling effect because it has some problems such as a fluid-structure interaction, influence by the free surface, vibration modes of structural panels and depth of water. In this paper, with fluid coupling effect, the effect of structural constraint between panels on the vibration characteristics are investigated numerically and discussed.

• Journal of Navigation and Port Research
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• v.26 no.1
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• pp.43-49
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• 2002

In this Paper, the mechanical behavior of two reかangular plates spot-welded under free vibration is investigated in detail. The focus of the analysis is to evaluate the effect of thickness of reinforced plates with equivalent thickness. The results of this the investigation are compared with detailed finite element analysis end experiments of the plates spot-welded for various parameters, such as aspect ratio, arm ratio, and distance ratio of spot-welding Points. The conclusion obtained are as followed. 1. The effect thickness due to spot-weld is very large, such as 55% in comparison with area ratio of spot-welding joint is just 4.52%. 2 The effect of thickness with respect to the distance ratio is maximized when the distance ratio is 0.4.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.12
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• pp.1356-1363
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• 2009

The aim of this research is to construct eigenfrequency optimization codes for plates with Arbitrary Rank Microstructures. From among noise factors, resonance sound is main reason for floor's solid noise. But, Resonance-elusion design codes are not fixed so far. Besides, The prediction of composite material's capability and an resonance elusion by controlling natural frequency of plate depend on designer's experiences. In this paper, First, using computer program with arbitrary rank microstructure, variation on composite material properties is studied, and then natural frequency control is performed by plate topology optimization method. The results of this study are as followed. 1) Programs that calculate material properties along it's microstructure composition and control natural frequency on composite material plate are coded by Homogenization and Topology Optimization method. and it is examined by example problem. 2) Equivalent material properties, calculated by program, are examined for natural frequency. In this paper, Suggested programs are coded using $Matlab^{TM}$, Feapmax and Feap Library with Homogenization and Topology Optimization method. and Adequacy of them is reviewed by performing the maximization or minimization of natural frequency for plates with isotropic or anisotropic materials. Since the programs has been designed for widely use. If the mechanism between composite material and other structural member is identified, extension application may be possible in field of structure maintenance, reinforcement etc. through application of composite material.

• Smart Structures and Systems
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• v.26 no.3
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• pp.331-343
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• 2020

In this paper, based on the CPT, motion equations for a sandwich plate containing a core and two integrated face-sheets have derived. The structure rests on the Visco-Pasternak foundation, which includes normal and shear modules. The piezo-magnetic core is made of CoFe₂O₄ and also is subjected to 3D magnetic potential. Two face sheets at top and bottom of the core are under electrical fields. Also, in order to obtain more accuracy, the effect of flexoelectricity has took into account at face sheets' relations in this work. Flexoelectricity is a property of all insulators whereby they polarize when subject to an inhomogeneous deformation. This property plays a crucial role in small-scale rather than macro scale. Employing CPT, Hamilton's principle, flexoelectricity considerations, the governing equations are derived and then solved analytically. By present work a detailed numerical study is obtained based on Piezoelectricity, Flexoelectricity and modified couple stress theories to indicate the significant effect of length scale parameter, shear correction factor, aspect and thickness ratios and boundary conditions on natural frequency of sandwich plates. Also, the figures show that there is an excellent agreement between present study and previous researches. These finding can be used for automotive industries, aircrafts, marine vessels and building industries.

• Journal of Korean Society of Steel Construction
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• v.18 no.2
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• pp.161-171
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• 2006

paper presents the results of a three-dimensional study of the natural vibration of laminated composite rectangular plates with various combinations of clamped and free boundaries. The Ritz method was used to obtain the stationary values of the associated Lagrangian, with displacements approximated using mathematicaly complete, characteristic orthogonal polynomials. The correctness of the three-dimensional model was established through a convergence study of the non-dimensional frequencies, followed by a comparison of the analytical findings in the existing literature. The wide scope of additional three-dimensional frequency results explains the influence of a number of geometrical and material parameters for angle-ply and cross-ply laminated plates, namely aspect ratio (${\mathcal{a/b}}$), thickness ratio (${\mathcal{a/h}}$), orthotropy of material, number of plies (${\mathcal{N}}$), fiber orientation angle (${\theta}$), and stacking sequence.

• Advances in nano research
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• v.10 no.5
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• pp.449-460
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• 2021

Flexoelectricity is an interesting materials' property that is more touchable in small scales. This property beside the sandwich structures placed in the center of scientists' attention due to their extraordinary effects on the mechanical properties. Furthermore, in the passage of decades, more elaborated sandwich structures took into consideration results from using honeycomb core. This kind of structure, inspiring from honeycomb core, provides more stiffness to weight ratio, which plays a crucial role in different industries. In this paper, based on the Love-Kirchhoff's hypothesis, Hamilton's principle, modified couple stress theory and Fourier series analytical method, equations of motion for a sandwich plate containing a honeycomb core integrated by two face-sheets have derived and solved analytically. The equations of both face sheets have derived by flexoelectricity consideration. Moreover, it should be noticed that the whole structure rests on the visco-Pasternak foundation. Conducting current research provided an acceptable and throughout study based on flexoelectricity to address the effect of materials' characteristics, length-scale parameter, aspect, and thickness ratios and boundary conditions on the natural frequency of honeycomb sandwich plates. Also, based on the presented figures and tables, there is a close agreement between previous studies and recent work. Due to the high ratio of strength to weight, current model analyzing is capable of taking into account for different vehicles' manufacturing in a high range of industries.