• Title/Summary/Keyword: Integral equation method

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The Characteristic of Electric Field Penetration into Infinite Conducting Plane with an Aperture Due to HEMP Incidence (HEMP 파원에 의한 무한 도체 평판 개구의 침투 전계 특성)

  • Lim, Byoung-Jin;Jung, Sung-Woo;Cho, Byung-Doo;Kim, Ki-Chai
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.21 no.12
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    • pp.1454-1459
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    • 2010
  • This paper presents the comparison of electric field penetration in Bell laboratories and IEC 61000-2-9 standard when HEMP source penetrates through an aperture in a planar conducting plane of infinite extent. HEMP electric field distributions assume in order to interpret this problem. Integral equation is derived and solved by Galerkin's method of moments for calculating the penetrating electric field. It is shown that penetrated electric field of IEC 61000-2-9 standard is greater than the Bell Laboratories waveform in resonance of lower frequency band, but those waveforms are similar in shape to frequency domain.

Inelastic Transient Dynamic Analysis of Two- and Three-dimensional Stress Problems by Particular Integral Boundary Element Method (로터 시스템 회전운동의 정식화 및 해석)

  • Yun, Seong-Ho;Ren, Li-Min
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.21 no.5
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    • pp.475-482
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    • 2008
  • This paper indicates that the use of Euler angles lacks in its consistency and exactness of analysis when it was applied to incorporate the rotational equation of motion for rotor systems by previous researcher. Kinetic energy and angular velocity are different from case to case depending on the way of choosing Euler angles and thus only the linear system has been investigated even though the rotor system has a very nonlinear behavior. A new methodology is applied by using both spherical coordinate and quaternion in the rotor rotation to overcome weaknesses of Euler angles and shows its superiority It is found through numerical examples that the use of quaternion will be a more useful and valid tool to derive the numerical model of the rotor system.

The Effect of Forebody Forms on the Ship Motion in Regular Head Waves (선형(船型)이 선체운동(船體運動)에 미치는 영향(影響)에 관(關)한 연구(硏究))

  • Jin-Ahn,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.12 no.1
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    • pp.47-58
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    • 1975
  • The effect of the bow shape on the ship motion response among longitudinal regular waves, is investigated employing the strip theory. The two dimensional hydrodynamic forces such as added mass and damping are calculated by the integral equation method for arbitrary sections. Nine ship models are selected for investigation. They are U, UV and V bow ship forms of different block coefficient of 0.6, 0.7 and 0.8 with constant after body. The heave amplitude of the V bow ship is smaller than that of the U bow ship in the whole range of wave length except extremely short wave as were stated by the earlier investigators. This results holds also in the case of bow vertical motions such as vertical relative displacement, velocity and acceralation. As to the pitch amplitudes, the V bow ship gives smaller value in long waves but larger value in short waves. However, heave and pitch phase angles are practically not influenced by the form of the fore body sections. In the bow motions, a little difference in phase angle is appeared in the vicinity of the wave which has same ship length. With respect to the wave exiting force and moment unfovourable effects could be expected in V bow ships. And these tendency hold also in the wave bending moment.

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Minimum Wave Resistance Hull Form Derived from Center Plane Source Distribution and its Application to Hull Form Design (선체중심선면(船體中心線面)에 분포(分布)된 특이점계(特異點系)로부터 얻어지는 최소조파저항선형(最少造波抵抗船型)과 그 응용(應用))

  • Hyo-Chul,Kim;B.S.,Hyun
    • Bulletin of the Society of Naval Architects of Korea
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    • v.19 no.4
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    • pp.31-37
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    • 1982
  • Developing a minimum wave resistance hull form which is satisfying the given requirements such as displacement and speed is one of the important problems in ship hydrodynamics. The theoretical approach conducted by Pien was successful in developing an optimized hull form, however, which can not be applied directly to practical hull form without manual lines fairing process. To avoid this difficulty, source distribution which arrived after the optimization was put into a fictitious restricted channel and as a result practicably modified hull form was derived by stream line tracing. The wave resistance of the hull thus obtained was calculated by solving the simplified integral equation suggested by Kan. The resistance at design point is almost same with that of the original hull which was represented by source distribution on the vertical rectangular center plane. It is therefore recommended to use the derived hull form for the hull which obtained after manual lines fairing process at Pienoid method. Further researches both in theory and experiment are necessary before this concept is put into practical application.

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A Numerical Model of Nonlinear Stream Function Wave Theory by the Least Squares Method (최소자승법을 사용한 유량함수 비선형 파랑이론의 수치모형)

  • 서승남
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.4
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    • pp.340-352
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    • 1994
  • A numerical model of nonlinear stream function wave theory evolved from Dean's model (1965) is presented. The stream function theory has been evaluated to be an accurate and useful tool for engineering applications. Effects of damping coefficient employed in a linearized simultaneous equation and number of points in the numerical integration of model on numerical solutions are assessed. Most accurate wave characteristics calculated by the present model are tabulated using revised Dean's Table (Chaplin, 1980) input parameters. Since the well-known feature of nearly breaking waves that with increasing wave steepness the wave length as well as integral properties have a maximum prior to the limiting wave height is represented by the model, the accuracy of model can be proved.

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Damage Detection in Composite Laminates using Tapping Sound (태핑음을 이용한 복합적층판의 손상검출)

  • Kim, Sung-Joon;Hong, Chang-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.37 no.11
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    • pp.1089-1095
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    • 2009
  • The radiated sound pressure induced by tapping test is obtained by solving the Rayleigh integral equation. For structurally radiated sound, the sound field is directly coupled to the structural motion. Therefore the impact response should be analyzed. In this paper, the delamination model is used to analyze the impact response of delaminated composite laminates. And efficient spring-mass model has been proposed to model hammer shaped impactor. Predicted sound pressure histories are compared with test data. The influence of damage on the sound pressure and impacted force history of laminates were investigated. The results show that both radiated sound pressure and impact force history are strongly influenced by delamination on laminates. As a result, it is shown that the presented sound based tapping method was found to be reliable for detecting the damage in composite laminate.

Propagation characteristics of longitudinal wave, shear wave and bending wave in porous circular nanoplates

  • Shan, Wubin;Deng, Zulu;Zhong, Hao;Mo, Hu;Han, Ziqiang;Yang, Zhi;Xiang, Chengyu;Li, Shuzhou;Liu, Peng
    • Structural Engineering and Mechanics
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    • v.76 no.4
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    • pp.551-559
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    • 2020
  • On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

Non-stationary vibration and super-harmonic resonances of nonlinear viscoelastic nano-resonators

  • Ajri, Masoud;Rastgoo, Abbas;Fakhrabadi, Mir Masoud Seyyed
    • Structural Engineering and Mechanics
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    • v.70 no.5
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    • pp.623-637
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    • 2019
  • This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

Development of TREND dynamics code for molten salt reactors

  • Yu, Wen;Ruan, Jian;He, Long;Kendrick, James;Zou, Yang;Xu, Hongjie
    • Nuclear Engineering and Technology
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    • v.53 no.2
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    • pp.455-465
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    • 2021
  • The Molten Salt Reactor (MSR), one of the six advanced reactor types of the 4th generation nuclear energy systems, has many impressive features including economic advantages, inherent safety and nuclear non-proliferation. This paper introduces a system analysis code named TREND, which is developed and used for the steady and transient simulation of MSRs. The TREND code calculates the distributions of pressure, velocity and temperature of single-phase flows by solving the conservation equations of mass, momentum and energy, along with a fluid state equation. Heat structures coupled with the fluid dynamics model is sufficient to meet the demands of modeling MSR system-level thermal-hydraulics. The core power is based on the point reactor neutron kinetics model calculated by the typical Runge-Kutta method. An incremental PID controller is inserted to adjust the operation behaviors. The verification and validation of the TREND code have been carried out in two aspects: detailed code-to-code comparison with established thermal-hydraulic system codes such as RELAP5, and validation with the experimental data from MSRE and the CIET facility (the University of California, Berkeley's Compact Integral Effects Test facility).The results indicate that TREND can be used in analyzing the transient behaviors of MSRs and will be improved by validating with more experimental results with the support of SINAP.

Static and stress analyses of bi-directional FG porous plate using unified higher order kinematics theories

  • Mohamed, Salwa;Assie, Amr E.;Mohamed, Nazira;Eltaher, Mohamed A.
    • Steel and Composite Structures
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    • v.45 no.3
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    • pp.305-330
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    • 2022
  • This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.