• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.637-654
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• 2011

The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh's statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, "new" modes are found to be a combination of the subsystem's modes (two rotations, traslation) and the bare plate's modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate's modes enable distinct motions of the 3-DOF system contributing differently to the "new' modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.

• Journal of Advanced Navigation Technology
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• v.4 no.2
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• pp.103-113
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• 2000

There are several methods in the mathematical modeling of a satellite with flexible appendages. In this paper, the hybrid Lagrange's equations of motion using assumed modes method are derived. The assumed modes method is one of approximate methods which have shorter calculation time due to low-dimension compare with FEM. These consist of three-equations about angular velocities and two-equations about flexible deformations, and physically represent interaction between hub and solar panel. In an attitude control, a control law is designed to minimize a given performance index considering not only control input but also vibration suppression. For these purpose, this paper applies LQG and LQG/LTR schemes to this model and finally show the capability for attitude control including vibration suppression. Especially, this paper shows the method of assumption as nonsingular system through singular value division for LQG/LTR design.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1101-1111
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• 2018

This study aims to present accurate soil modeling and validation of a single roadside guardrail post as well as a single concrete pile installed near cut slopes or compacted sloping embankment. The conventional Winkler's elastic spring model and p-y curve approach for horizontal ground cannot directly be applied to sloping ground where ultimate soil resistance is significantly dependent on ground inclination. In this study, both grid-based 3-D FE model and particle-based SPH (smoothed particle hydrodynamics) model available in LS-DYNA have been adopted to predict the static behavior of a laterally loaded guardrail post. The SPH model has potential to eliminate any artificial soil stiffness due to the deterioration of the node-connected Lagrangian soil mesh. For this purpose, this study comprises two parts. Firstly, only 3-D FE modeling has been tested to show the numerical validity for a single concrete pile in sloping ground using Mohr-Coulomb material. However, this material option cannot be implemented for SPH elements. Nevertheless, Mohr-Coulomb model has been used since this material model requires six input soil data that can be obtained from the comparative papers in literatures. Secondly, this work is extended to compute the lateral resistance of a guardrail post located near the slope using the hybrid approach that combines Lagrange FE elements and SPH elements by the suitable node-merging option provided by LS-DYNA. For this analysis, the FHWA soil material developed for application to road-base soils has been used and also allows the application of SPH element.

• Advances in nano research
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• v.15 no.5
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• pp.401-410
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• 2023

Vibration investigation of fluid-filled three layered cylindrical shells is studied here. A cylindrical shell is immersed in a fluid which is a non-viscous one. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the wave propagation approach procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped (C-C), simply supported-simply supported (SS-SS) frequency curves are higher than that of clamped-simply (C-S) curves. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Computer software MATLAB codes are used to solve the frequency equation for extracting vibrations of fluid-filled.

• Economic and Environmental Geology
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• v.14 no.2
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• pp.93-102
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• 1981

Studies of model potential fields continued upward and downward show differences depending on the method of continuation. Beginning with a magnetic field computed over a buried vertical cylinder, the field was continued to various levels by a method introduced by Henderson (Lagrangian interpolation) and by a spectral method (frequency domain analysis). Resultant fields show (1) no significant differences in upward continued values, (2) in downward continuation, accurate values are obtained with the spectral method over the central part of the anomaly, and (3) accurate values are obtained with Henderson's method on the flanks of the anomaly, while oscillations usually characterize the spectral method in this region. Essentially the same observations are made for derivative calculations. Field oscillations are empirically predicted at levels continued to approximately two-thirds of the depth of the source. Our spectral computer program output yields marked oscillations at one-half of the depth of the source. Henderson's method shows no oscillations at this depth and only minor oscillations at the top of the body (some negative values appear on the flanks of the anomaly). The Henderson output is a smooth field even if continued below the top of the body. These results suggest that the presence of oscillations cannot be used to identify the top of a buried source without careful consideration of the method used to continue the field. Use of the derivative to outline and isolate anomalies must similarly include consideration of the method of calculation.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.5
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• pp.217-227
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• 2017

The object of this study is to estimate the net volume transport and the residual flow that changed by space and time at southern part of Yeomha channel, Gyeonggi Bay. The cross-section observation was conducted at the mid-part (Line2) and the southern end (Line1) of Yeomha channel for 13 hours during neap and spring-tides, respectively. The Lagrange flux is calculated as the sum of Eulerian flux and Stokes drift, and the residual flow is calculated by using least square method. It is necessary to unify the spatial area of the observed cross-section and average time during the tidal cycle. In order to unify the cross-sectional area containing such a large vertical tidal variation, it was necessary to convert into sigma coordinate system by horizontally and vertically for every hour. The converted sigma coordinate system is estimated to be 3~5% error when compared with the z-level coordinate system which shows that there is no problem for analyzing the data. As a result, the cross-sectional residual flow shows a southward flow pattern in both spring and neap tides at Line2, and also have characteristic of the spatial residual flow fluctuation: it northwards in the main line direction and southwards at the end of both side of the waterway. It was confirmed that the residual flow characteristics at Line2 were changed by the net pressure due to the sea level difference. The analysis of the net volume transport showed that it tends to southwards at $576m^3s^{-1}$, $67m^3s^{-1}$ in each spring tide and neap tide at Line2. On the other hand, in the control Line1, it has tendency to northwards at $359m^3s^{-1}$ and $248m^3s^{-1}$. Based on the difference between the two observation lines, it is estimated that net volume transport will be out flow about $935m^3s^{-1}$ at spring tide stage and about $315m^3s^{-1}$ at neap tide stage as the intertidal zone between Yeongjong Island and Ganghwa Island. In other words, the difference of pressure gradient and Stokes drift during spring and neap tide is main causes of variation for residual current and net volume transport.

• Journal of the Korean Institute of Gas
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• v.6 no.1 s.17
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• pp.1-9
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• 2002

This paper presents simple models for flow and the PIG dynamics when it passes through a $90^{\circ}$ curved section of pipeline. The simulation has been done with two different operational boundary conditions. The solution fur non-linear hyperbolic partial equations for flow is given by using MOC. The Runge-Kuta method is used to solve the initial condition equation fur flow and the PIG dynamics equation. The simulation results show that the proposed model and solution can be used fur estimating the PIG dynamics when the pig runs in the pipeline including curved section. In this paper, dynamic modeling and its analysis for the PIG flow through $90^{\circ}$ curved pipe with compressible and unsteady flow are studied. The PIG dynamics model is derived by using Lagrange equation under assumption that it passes through 3 different sections in the curved pipeline such that it moves into, inside and out of the curved section. The downstream and up stream flow dynamics including the curved sections are solved using MOC. The effectiveness of the derived mathematical models is estimated by simulation results fur a low pressure natural gas pipeline including downward and upward curved sections. The simulation results show that the proposed model and solution can be used for estimating the PIG dynamics when we pig the pipeline including curved section.

• Journal of Satellite, Information and Communications
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• v.11 no.2
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• pp.55-59
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• 2016

Conventional RF energy harvesting systems can harvest energy and decode information from same source as an Hybirid-AP (H-AP). However, harvesting efficiency is seriously dependent on distance between users and H-AP. Therefore, in this paper, we proposed a transmission model for RF harvesting consisting of information and power source separately called Decoupled RF Energy harvesting networks. Main purpose of this paper is to maximize energy efficiency under various constraints of transmit power from H-AP and power beacon (PB), minimum quality of service and quality of harvested power of each users. To measure proposed model's performance, we proposed optimal time scheduling algorithms for energy efficiency (EE) maximization using Lagrangian dual decomposition theory that locally maximizes the EE by obtaining suboptimal values of three arguments : transmit power of H-AP, transmit power of PB, frame splitting factor. Experiment results show that the proposed energy-efficient algorithms converge within a few iterations with its optimality and greatly improve the EE compared to that of baseline schemes.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.5
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• pp.93-101
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• 2010

The effects of braking of trains and roughness of rails on the dynamic behavior of bridges are studied. The train-bridge interaction is considered by solving Lagrange's equation of motions. Newmark's direct integration is used to solve the governing equations. Dynamic train loads acting on piers at each time step are evaluated, and the wheel-rail roughness effect is considered by using the PSD curve of the rail. The model of braking forces in bridge section is based on the change of deceleration mentioned in ASTM(American Society for Testing and Materials) E503-82. Only skidding frictions without considering rolling frictions are modeled, and the friction coefficient of 0.25 is assumed. Parametric studies in a simply supported PC Box girder bridge are carried out to verify the present method and to analyze the effects of train speed, wheel-rail roughness, braking forces on dynamic train loads.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.