• Title/Summary/Keyword: One Equation Method

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A comprehensive analysis on the discretization method of the equation of motion in piezoelectrically actuated microbeams

  • Zamanian, M.;Rezaei, H.;Hadilu, M.;Hosseini, S.A.A.
    • Smart Structures and Systems
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    • v.16 no.5
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    • pp.891-918
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    • 2015
  • In many of microdevices a part of a microbeam is covered by a piezoelectric layer. Depend on the application a DC or AC voltage is applied between upper and lower side of the piezoelectric layer. A common method in many of previous works for evaluating the response of these structures is discretizing by Galerkin method. In these works often single mode shape of a uniform microbeam i.e. the microbeam without piezoelectric layer has been used as comparison function, and so the convergence of the solution has not been verified. In this paper the Galerkin method is used for discretization, and a comprehensive analysis on the convergence of solution of equation that is discretized using this comparison function is studied for both clamped-clamped and clamped-free microbeams. The static and dynamic solution resulted from Galerkin method is compared to the modal expansion solution. In addition the static solution is compared to an exact solution. It is denoted that the required numbers of uniform microbeam mode shapes for convergence of static solution due to DC voltage depends on the position and thickness of deposited piezoelectric layer. It is shown that when the clamped-clamped microbeam is coated symmetrically by piezoelectric layer, then the convergence for static solution may be obtained using only first mode. This result is valid for clamped-free case when it is covered by piezoelectric layer from left clamped side to the right. It is shown that when voltage is AC then the number of required uniform microbeam shape mode for convergence is much more than the number of required mode in modal expansion due to the dynamic effect of piezoelectric layer. This difference increases by increasing the piezoelectric thickness, the closeness of the excitation frequency to natural frequency and decreasing the damping coefficient. This condition is often indefeasible in microresonator system. It is concluded that discreitizing the equation of motion using one mode shape of uniform microbeam as comparison function in many of previous works causes considerable errors.

Structural Equation Model Analysis of Communication Ability by Havruta Teaching-Learning Method

  • Jae-Nam Kim;Seong-Eun Chu
    • Journal of the Korea Society of Computer and Information
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    • v.28 no.10
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    • pp.197-205
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    • 2023
  • This study is to apply the Havruta teaching-learning method to college students' major classes and analyze the relationship between the effectiveness evaluation of communication skills and sub-factors using a structural equation model. As a result of the study, the communication ability score was different before and after Havruta teaching-learning, and it was found that after Havruta teaching-learning was higher than before Havruta teaching-learning. The path effect was found to be significant in all of the total, direct, and indirect effects among latent variables, except for the relationship between interpretation ability, role-playing ability, and goal-setting ability in the direct effect. In this study, it was found that the Havruta teaching-learning method not only improves creativity and thinking ability, but also improves self-directed learning ability. In addition, it was reconfirmed that it is a teaching-learning method that can develop social skills and communication skills as well as problem-solving skills while experiencing opinions different from one's own. As a result, research on a thorough student-centered teaching-learning method suitable for the Homo Machina era must be continued and its application in the educational field must be implemented.

Development of a GIS Method for the Automatic Calculation of LS Factor of USLE (GIS를 이용한 USLE 지형인자(LS) 자동계산 방법에 관한 연구)

  • 우창호;황국웅
    • Journal of the Korean Institute of Landscape Architecture
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    • v.26 no.3
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    • pp.162-177
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    • 1998
  • Conentionally, LS factor for the USLE suggested by Wischmeier has been computed manually on topographic maps based on one dimensional approach. But outcomes of the equation could be severely affected by the convergence and divergence of surface runoff at complex terrains. Thus the objective of this research are to develop a method to automatically compute LS factor based on the multiple flow algorithm, and to test the accuracy of this method by comparing outcomes of this method to previous measurements or estimations of soil erosion. The program for the automatic calculation of LS factor was developed by utilizing Fox Pro 4.5, and outcomes of the program is designed to input to IDRISI. The accuracy test of LS factor was carried out by comparing the actual measurements of soil loss at two test sites in and around of Suwon. The calculated volume of soil erosion at Buju mountain, Mokpo, was also compared to the outcome of a previous research based on the LS factor calculated by the conventional onedimensional approach. The outcomes of this research are as follows. First, the computed L based on the multiple flow algorithm for concae slopes are greater than those of convex slopes,. Second, the estimated soil loss based on this method at the test site in Mokpo is much greater than the outcomes based on the conventional one-dimensional approach. It can e concluded that the application of this automatic calculation method of LS factor can improve the accuracy of USLE and facilitate soil erosion prevention methods.

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Experimental Vibration Analysis of a Super-Structure Model Using Curve Fitting Method (곡선맞춤법을 이용한 선체상부구조 모델의 진동해석)

  • Oh, Chang-Geun;Je, Hae-Kwang;Park, Sok-Chu
    • Journal of Navigation and Port Research
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    • v.26 no.3
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    • pp.281-288
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    • 2002
  • It might be true that both experimental and analytic techniques have been developed in the vibration analysis end engineering. It could not be said, however, that the experimental method has been also developed as much as analytic method, such as Finite Element Method One of the reason is that computation time becomes longer and that the solution often diverges depending on the choice of initial value in solving nonlinear equation. The equation in experimental modal analysis is usually composed of the nonlinear term of natural frequency and modal damping ratio, and the linear one of equivalent stiffness. In this study, the nonlinear terms were solved first, and then the linear term was obtained. The experimental modal parameters were estimated, applying the developed experimental modal analysis curve-fitting method to the super-structure model. In addition, the number of modes and modal damping ratio could be easily determined by the developed program with the application of graphical techniques and with easy handling button.

Estimation of Agricultural Reservoir Water Storage Based on Empirical Method (저수지 관리 관행을 반영한 농업용 저수지 저수율 추정)

  • Kang, Hansol;An, Hyunuk;Nam, Wonho;Lee, Kwangya
    • Journal of The Korean Society of Agricultural Engineers
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    • v.61 no.5
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    • pp.1-10
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    • 2019
  • Due to the climate change the drought had been occurring more frequently in recent two decades as compared to the previous years. The change in the pattern and frequency of the rainfall have a direct effect on the farming sector; therefore, the quantitative estimation of water supply is necessary for efficient agricultural water reservoir management. In past researches, there had been several studies conducted in estimation and evaluation of water supply based on the irrigational water requirement. However, some researches had shown significant differences between the theoretical and observed data based on this requirement. Thus, this study aims to propose an approach in estimating reservoir rate based on empirical method that utilized observed reservoir rate data. The result of these two methods in comparison with the previous one is seen to be more fitted for both R2 and RMSE with the observed reservoir rate. Among these procedures, the method that considers the drought year data shows more fitted outcomes. In addition, this new method was verified using 15-year (2002 to 2006) linear regression equation and then compare the preceeding 3-year (1999 to 2001) data to the theoretical method. The result using linear regression equation is also perceived to be more closely fitted to the observed reservoir rate data than the one based on theoretical irrigation water requirement. The new method developed in this research can therefore be used to provide more suitable supply data, and can contribute to effectively managing the reservoir operation in the country.

Travel Time Calculation Using Mono-Chromatic Oneway Wave Equation (단일주파수 일방향파동방정식을 이용한 주시계산)

  • Shin, Chang-Soo;Shin, Sung-Ryul;Kim, Won-Sik;Ko, Seung-Won;Yoo, Hai-Soo
    • Geophysics and Geophysical Exploration
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    • v.3 no.4
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    • pp.119-124
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    • 2000
  • A new fast algorithm for travel time calculation using mono-chromatic one-way wave equation was developed based on the delta function and the logarithms of the single frequency wavefield in the frequency domain. We found an empirical relation between grid spacing and frequency by trial and error method such that we can minimize travel time error. In comparison with other methods, travel time contours obtained by solving eikonal equation and the wave front edge of the snapshot by the finite difference modeling solution agree with our algorithm. Compared to the other two methods, this algorithm computes travel time of directly transmitted wave. We demonstrated our algorithm on migration so that we obtained good section showing good agreement with original model. our results show that this new algorithm is a faster travel time calculation method of the directly transmitted wave for imaging the subsurface and the transmission tomography.

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Numerical Study on the Reflection of a Solitary Wave by a Vertical Wall Using the Improved Boussinesq Equation with Stokes Damping (고립파의 수직 벽면 반사와 Stokes 감쇠에 관한 개선된 부시네스크 방정식을 이용한 수치해석 연구)

  • Park, Jinsoo;Jang, Taek Soo
    • Journal of the Society of Naval Architects of Korea
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    • v.59 no.2
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    • pp.64-71
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    • 2022
  • In this paper, we simulate the collision of a solitary wave on a vertical wall in a uniform water channel and investigate the effect of damping on the amplitude attenuation. In order to take into account the damping effect, we introduce the Stokes damping whose dissipation is dependent on the velocity of wave motion on the surface of a thin layer of oil. That is, we use the improved Boussinesq equation with Stokes damping to describe the damped wave motion. Our work mainly focuses on the amplitude attenuation of a propagating solitary wave, which may depend on the Stokes damping together with the initial position and initial amplitude of the wave. We utilize the method of images and a powerful numerical tool (functional iteration method) for solving the improved Boussinesq equation, yielding an effective numerical simulation. This enables us to find the amplitudes of the incident wave and reflected one, whose ratio is a measure of the (wave) amplitude attenuation. Accordingly, we have shown that the reflection of a solitary wave by a vertical wall is dependent on not only the initial amplitude and position of a solitary but the Stokes damping.

A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams

  • Du, Mengjie;Liu, Jun;Ye, Wenbin;Yang, Fan;Lin, Gao
    • Structural Engineering and Mechanics
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    • v.81 no.2
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    • pp.179-194
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    • 2022
  • The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

Topology Optimization of Electromagnetic Systems with Two Materials (전자기 시스템에서 두 가지 물성치를 고려한 위상최적설계 기법)

  • Kang, Je-Nam;Wang, Se-Myung
    • Proceedings of the KIEE Conference
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    • 2002.07b
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    • pp.726-728
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    • 2002
  • The topology optimization of electromagnetic systems with two materials is investigated using the FEM. The design sensitivity equation for topology optimization is derived using the adjoint variable method and the continuum approach. The proposed method is applied to the topology optimization of C-core and compared to previous study with one material.

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On the Dynamic Stability of Rectangular Plates with Four Free Edges Subjected to Pulsating Follower Forces (맥동종동력이 작용하는 사각 자유경계판의 동적 안정성에 관한 연구)

  • 추연선;김지환
    • Journal of KSNVE
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    • v.7 no.1
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    • pp.127-134
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    • 1997
  • The dynamic stability of classical plates and Mindlin plates subjected to pulsating follower forces is investigated in this paper. Using the finite element method, the induced equation is reduced to that of one with finite degrees of freedom. Then, the multiple scales method is applied to analyze the dynamic instability region. The effects of aspect ratio, Poisson ratio, rotary inertia and shear deformation on the dynamic stability of plates are studied in this paper.

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