• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• Structural Engineering and Mechanics
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• v.91 no.6
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• pp.551-565
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• 2024

This study presents a methodical investigation into improving structural designs through the analytical examination of the dynamic behavior of functionally graded plates (FGPs) resting on viscoelastic foundations. By employing a four variable first-order shear deformation theory, the study computes non-dimensional frequencies for a variety of porous FGPs with diverse graded patterns and porosity distributions. Different gradient patterns of the plates are considered, and three distinct functions-sigmoid (S-FGM), exponential (E-FGM), and power-law (P-FGM)-are utilized to assess material performance in specific directions. The equations of motion are derived and solved using both Navier's method and Hamilton's principle. Analytical solutions for vibration frequency are provided to validate the proposed methodology against existing literature. Furthermore, a comprehensive parametric analysis is conducted, taking into account various factors such as ceramic material, porosity distribution, gradient index, length-to-thickness ratio, gradient pattern, and damping coefficient. The findings suggest that enhancing the damping coefficient of the viscoelastic foundation can significantly improve the free-vibrational response of functionally graded material plates.

• Journal of the Korean Geotechnical Society
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• v.15 no.6
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• pp.167-185
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• 1999

A series of model tests was performed to find the characteristics of lateral behavior of single rigid pile. This paper shows the results of model tests on the lateral behavior of single rigid driven pile in non-homogeneous(two layered) Nak-Dong River sands. The purpose of this paper is to investigate the effect of the ratio of lower layer thickness to embedded pile length, the coefficient ratio of the subgrade reaction and the pile construction conditions(driven & embedded piles) on the characteristics of lateral behavior of single pile. The results of model tests show that the lateral behavior in non-homogeneous soil depends upon drop energy considerably, that is, in the case of H/L=0.75, as the drop energy increases three times the decrease percentage increases about 2.12 times. In the driven pile with non-homogeneous soil of $E_{h1}/E_{h2}=5.56$, the effect of upper layer with large stiffness on the decrease of lateral deflection is remarkably smaller than embedded pile. In non-homogeneous soil, the maximum bending moment of driven pile is in the range of 100 132% in comparison with embedded pile. The reason is that the stiffness of soil around pile increases with drop vibration and so the pile behavior is similar to the flexible pile behavior by means of the increase of relative stiffness of pile, In this paper, the experimental equations for lateral load and H/L on $y_D/y_E \; & \; MBM_D/MBM_E$ are suggested from model tests.

• Composites Research
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• v.13 no.2
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• pp.30-39
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• 2000

It is difficult for civil engineer to apply composite materials of laminated type to structure for civil construction because of complicated theory although those have much merit. A simple method by which one can predict "exact" values of the natural frequency of vibration of laminated plates is presented. Many laminates with particular orientations have negligible values of $B_{16}$ and $B_{26}$ as the number of plies increases. Such laminates, with $D_{16}$ = $D_{26}$ ->0 can be solved by the same equation as for the special orthotropic laminates(1991,1995). If the quasi-isotrpic constants are used, It is possible to simplify analysis procedure since the equations for isotropic plates can be used. Use of some coefficients can produce "exact" values for laminates with such configuration. This coefficient, in fact, represents the effect of the anisotropy of the laminate. D. H. Kim proposed to use a correction factor, he developed, to produce "exact" solution out of the approximate solution obtained by using the quasi-isotropic constants(1995). In this paper, the fiber orienation studied is [$\alpha$/$\beta$/$\beta$/$\gamma$/$\alpha$/$\alpha$/$\beta$]r, with $\alpha$=-$\beta$, and $\gamma$${\gamma}$=$0^{\circ}$ or $90^{\circ}$ and the above-mentioned method is used to obtain the natural frequencies of plates with such orientations, and detailed result is presented for the use of engineers.nted for the use of engineers.

• Journal of Korean Tunnelling and Underground Space Association
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• v.17 no.3
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• pp.319-332
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• 2015

The pressure wave formed by the piston effects of the train proceeds within the tunnel when a train enters the tunnel with a high speed. Depending on the condition of tunnel exit, the compression waves reflect at a open end, change to the expansion waves, transfer to tunnel entrance back. Due to interference in the pressure waves and running train, passengers experience severe pressure fluctuations. And these pressure waves result in energy loss, noise, vibration, as well as in the passengers' ears. In this study, we performed comparison between numerical analysis and field experiments about the characteristics of the pressure waves transport in tunnel that appears when the train enter a tunnel and the variation of pressure penetrating into the train staterooms according to blockage ratio of train. In addition, a comparative study was carried out with the ThermoTun program to examine the applicability of the compressible 1-D model(based on the Method of Characteristics). Furthermore examination for the adequacy of the governing equations analysis based on compressible 1-D numerical model by Baron was examined.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.4 s.44
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• pp.19-28
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• 2005

Long span structures with low natural frequencies such as shopping malls, large offices, and assembly rooms may experience signification dynamic responses due to human activities. In many cases, the group activities are common thing in comparison with the single activity. The purpose of this study is to evaluate the responses of building structure subjected to group human loads using mode shapes. For this purpose, equations to estimate the magnitudes ol responses ol structure subjected to group walking loads are derived. And the correlation of loads is verified for identifying the relation of each human load composing of group human loads using two load cells. The method is proposed for evaluating the responses of structure subjected to group loads using mode shapes and correlation function related to each human loads. The effectiveness ol the proposed method is verified analytically using a simple beam and floor and experimentally on a footbridge measuring the structural response induced by group pedestrians for the case of synchronization or not. Results indicate that the amplitudes of group walking loads can be easily estimated if the mode shapes are available, and that the corresponding structural responses can be estimated easily by the simple response measurement using the proposed method.

• Journal of KSNVE
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• v.8 no.5
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• pp.964-973
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• 1998

In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.2
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• pp.21-27
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• 2003

In general, simple fluid added mass method is used for the seismic and vibration analysis of the immersed structure to consider the fluid-structure interaction effect. Actually, the structural response of the immersed structure can be affected by both the fluid added mass and damping caused by the fluid viscosity. These variables appeared as a consistent matrix form with the coupling terms. In this paper, finite element formula for the inviscid fluid case and viscous fluid case are derived from the linearized Navier Stoke's equations. Using the finite element program developed in this paper, the analyses of fluid added mass and damping for the hexagon core structure of the liquid metal reactor are carried out to investigate the effect of fluid viscosity with variation of the fluid gap and Reynolds number. From the analysis results, it is verified that the viscosity significantly affects the fluid added mass and damping as the fluid gap size decrease. From the analysis results of eccentricity effect on the fluid added mass and damping of the concentric cylinders, the fluid added mass increase as the eccentricity increases, however the fluid damping increases only when the eccentricity is very severe.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.2
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• pp.23-33
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• 2011

In this study, a CFPBS (Cone-type Friction Pendulum Bearing System) was developed which controls the acceleration delivered to the structure to prevent damage and degradation of the critical communication equipment in case of an earthquake. The isolation performance of the CFPBS was evaluated by numerical analysis. The CFPBS was manufactured in the shape of a cone differenced from the existing FPS (Friction Pendulum System), and a pattern was engraved on the friction surface. The natural frequencies of the CFPBS were evaluated from a free-vibration test with the seismic isolator system consisting of four CFPBSs. In order to verify its earthquake-resistant performance, a numerical analysis program was created from the equation of the CFPBS induced from the equations of motion. A simplified theoretical equation of the CFPBS was proposed to manufacture the equipment which could demonstrate the necessary performance. Artificial seismic waves satisfying the maximum earthquake scale of the Korean Building Code-Structural (KBC-2005) were created and verified to review the earthquake-resistant performance of the CFPBS by numerical analysis. The superstructural mass of the CFPBS and skew angle of the friction surface were considered for numerical analysis with El Centro NS (1940), Kobe NS (1995) and artificial seismic waves. The CFPBS isolation performance evaluation was based on the results of numerical analysis and the executed comparative analysis between the results from numerical analysis and the simplified theoretical equation under the same conditions.

• Journal of the Korean Geotechnical Society
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• v.29 no.2
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• pp.35-45
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• 2013

The void ratio is an important parameter for reflecting the soil behavior including physical property, compressibility, and relative density. The void ratio can be obtained by laboratory test with extracted soil samples. However, the specimen has a possibility to be easily disturbed due to the stress relief when extracting, vibration during transportation, and error in experimental process. Thus, the theoretical equations have been suggested for obtaing the void ratio based on the elastic wave velocities. The objective of this paper is to verify the accuracy of the proposed analytical solution through the error norm. The paper covers the theoretical methods of Wood, Gassmann and Foti. The elastic wave velocity is determined by the Field Velocity Probe in the southern part of Korean Peninsular. And the rest parameters are assumed based on the reference values. The Gassmann method shows the high reliability on determining the void ratio. The error norm is also analyzed as substitution of every parameter. The results show every equation has various characteristics. Thus, this paper may be widely applied for obtaining the void ratio according to the field condition.