• Title/Summary/Keyword: Integral equation

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A Analysis on the Estimation Method of the 3D Underwater Radiation Noise Pattern of Cylindrical Structure with the Underwater Experiments (수중실험을 통한 원통구조물의 3차원 수중방사소음 패턴 산출기법 분석)

  • Yi, Jongju;Kang, Myunghwan;Han, Seungjin;Jeong, Hyunjoo;Oh, Junseok;Bae, Sooryong;Jung, Woojin;Seo, Young Soo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.24 no.11
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    • pp.907-918
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    • 2014
  • In this study for the prediction of 3D underwater radiated noise pattern, a comparison between the proposed method(DHIE, Discrete Helmholtz Integral Equation) and the 3D underwater radiated noise calculation results using the measurement of near-field acoustic pressure data is performed. The near-field acoustic pressure in water is measured for the calculation of the far-field radiated noise pattern and the far-field acoustic power. Also the vibration field of the underwater structure is measured in simultaneously. Using the total far-field acoustic power and the vibration field on the surface of the structure, the proposed method(DHIE) can predict the underwater radiated noise pattern of the far-field The predicted results show the reasonable agreement within about 5dB comparing with the experiment result.

On the Removal of Irregular Frequencies in the Prediction of Ship Motion in Waves (파랑중에서 전진동요하는 선박의 특이파수 억제에 관한 연구)

  • H.Y. Lee;D.J. Yum
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.4
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    • pp.73-81
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    • 1994
  • The source and source/dipole distribution methods using 3-dimensional panel method have been widely used for ship motion analysis. When these methods are used, large errors in the predicted hydrodynamic coefficients are introduced around the irregular frequencies caused by the resonance of imaginary internal flow. Therefore, the irregular frequencies need to be removed for an accurate prediction of ship motion. This paper adopts 3-dimensional translating and oscillating Green function derived by Wu. The adaptive integration method, stretching transform and stationary phase method are used for the calculation of the calculation of Green function and the integral equation is derived by distributing the Green function n ship surface and inner free-surface. The condition of zero normal velocity, that is, wall condition on inner free-surface has been successfully used for the removal of irregular frequencies in oscillating problems. The calculations are carried out for series 60($C_B=0.7$) vessel and the results are compared with those of other theoretical analyses and experiment.

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Reassessment of viscoelastic response in steel-concrete composite beams

  • Miranda, Marcela P.;Tamayo, Jorge L.P.;Morsch, Inacio B.
    • Structural Engineering and Mechanics
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    • v.81 no.5
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    • pp.617-631
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    • 2022
  • In this paper the viscoelastic responses of four experimental steel-concrete composite beams subjected to highly variable environmental conditions are investigated by means of a finite element (FE) model. Concrete specimens submitted to stepped stress changes are also evaluated to validate the current formulations. Here, two well-known approaches commonly used to solve the viscoelastic constitutive relationship for concrete are employed. The first approach directly solves the integral-type form of the constitutive equation at the macroscopic level, in which aging is included by updating material properties. The second approach is postulated from a rate-type law based on an age-independent Generalized Kelvin rheological model together with Solidification Theory, using a micromechanical based approach. Thus, conceptually both approaches include concrete hardening in two different manners. The aim of this work is to compare and analyze the numerical prediction in terms of long-term deflections of the studied specimens according to both approaches. To accomplish this goal, the performance of several well-known model codes for concrete creep and shrinkage such as ACI 209, CEB-MC90, CEB-MC99, B3, GL 2000 and FIB-2010 are evaluated by means of statistical bias indicators. It is shown that both approaches with minor differences acceptably match the long-term experimental deflection and are able to capture complex oscillatory responses due to variable temperature and relative humidity. Nevertheless, the use of an age-independent scheme as proposed by Solidification Theory may be computationally more advantageous.

Effects of inclined bedrock on dissimilar pile composite foundation under vertical loading

  • Kaiyu, Jiang;Weiming, Gong;Jiang, Xu;Guoliang, Dai;Xia, Guo
    • Geomechanics and Engineering
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    • v.31 no.5
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    • pp.477-488
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    • 2022
  • Pile composite foundation (PCF) has been commonly applied in practice. Existing research has focused primarily on semi-infinite media having equal pile lengths with little attention given to the effects of inclined bedrock and dissimilar pile lengths. This investigation considers the effects of inclined bedrock on vertical loaded PCF with dissimilar pile lengths. The pile-soil system is decomposed into fictitious piles and extended soil. The Fredholm integral equation about the axial force along fictitious piles is then established based on the compatibility of axial strain between fictitious piles and extended soil. Then, an iterative procedure is induced to calculate the PCF characteristics with a rigid cap. The results agree well with two field load tests of a single pile and numerical simulation case. The settlement and load transfer behaviors of dissimilar 3-pile PCFs and the effects of inclined bedrock are analyzed, which shows that the embedded depth of the inclined bedrock significantly affects the pile-soil load sharing ratios, non-dimensional vertical stiffness N0/wdEs, and differential settlement for different length-diameter ratios of the pile l/d and pile-soil stiffness ratio k conditions. The differential settlement and pile-soil load sharing ratios are also influenced by the inclined angle of the bedrock for different k and l/d. The developed model helps better understand the PCF characteristics over inclined bedrock under vertical loading.

Spatial Estimation of soil roughness and moisture from Sentinel-1 backscatter over Yanco sites: Artificial Neural Network, and Fractal

  • Lee, Ju Hyoung
    • Proceedings of the Korea Water Resources Association Conference
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    • 2020.06a
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    • pp.125-125
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    • 2020
  • European Space Agency's Sentinel-1 has an improved spatial and temporal resolution, as compared to previous satellite data such as Envisat Advanced SAR (ASAR) or Advanced Scatterometer (ASCAT). Thus, the assumption used for low-resolution retrieval algorithms used by ENVISAT ASAR or ASCAT is not applicable to Sentinel-1, because a higher degree of land surface heterogeneity should be considered for retrieval. The assumption of homogeneity over land surface is not valid any more. In this study, considering that soil roughness is one of the key parameters sensitive to soil moisture retrievals, various approaches are discussed. First, soil roughness is spatially inverted from Sentinel-1 backscattering over Yanco sites in Australia. Based upon this, Artificial Neural Networks data (feedforward multiplayer perception, MLP, Levenberg-Marquadt algorithm) are compared with Fractal approach (brownian fractal, Hurst exponent of 0.5). When using ANNs, training data are achieved from theoretical forward scattering models, Integral Equation Model (IEM). and Sentinel-1 measurements. The network is trained by 20 neurons and one hidden layer, and one input layer. On the other hand, fractal surface roughness is generated by fitting 1D power spectrum model with roughness spectra. Fractal roughness profile is produced by a stochastic process describing probability between two points, and Hurst exponent, as well as rms heights (a standard deviation of surface height). Main interest of this study is to estimate a spatial variability of roughness without the need of local measurements. This non-local approach is significant, because we operationally have to be independent from local stations, due to its few spatial coverage at the global level. More fundamentally, SAR roughness is much different from local measurements, Remote sensing data are influenced by incidence angle, large scale topography, or a mixing regime of sensors, although probe deployed in the field indicate point data. Finally, demerit and merit of these approaches will be discussed.

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Linear Spectral Method for Simulating the Generation of Regular Waves by a Moving Bottom in a 3-dimensional Space (3차원 공간에서 바닥의 움직임에 의한 규칙파의 생성을 모의할 수 있는 선형 스펙트럼법)

  • Jae-Sang Jung;Changhoon Lee
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.36 no.2
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    • pp.70-79
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    • 2024
  • In this study, we introduce a linear spectral method capable of simulating wave generation and transformation caused by a moving bottom in a 3-dimensional space. The governing equations are linear dynamic free-surface boundary conditions and linear kinematic free-surface boundary conditions, which are solved in Fourier space. Solved velocity potential and free-surface displacement should satisfy continuity equation and kinematic bottom boundary condition. For numerical analysis, a 4th order Runge-Kutta method was utilized to analyze the time integral. The results obtained in Fourier space can be converted into velocity potential and free-surface displacement in a real space using inverse Fourier transform. Regular waves generated by various types of moving bottoms were simulated with the linear spectral method. Additionally, obliquely generated regular waves using specified bottom movements were simulated. The results obtained from the spectral method were compared to analytical solutions, showing good agreement between the two.

Fracture and Hygrothermal Effects in Composite Materials (복합재의 파괴와 hygrothermal 효과에 관한 연구)

  • Kook-Chan Ahn;Nam-Kyung Kim
    • Journal of the Korean Society of Safety
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    • v.11 no.4
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    • pp.143-150
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    • 1996
  • This is an explicit-Implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE ) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for and existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The Ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory Darcy's law Is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full newton-Raphson method is used for solving the nonlinear governing equations.

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Fluid bounding effect on FG cylindrical shell using Hankel's functions of second kind

  • Khaled Mohamed Khedher;Shahzad Ali Chattah;Mohammad Amien Khadimallah;Ikram Ahmad;Muzamal Hussain;Rana Muhammad Akram Muntazir;Mohamed Abdelaziz Salem;Ghulam Murtaza;Faisal Al-Thobiani;Muhammad Naeem Mohsin;Abeera Talib;Abdelouahed Tounsi
    • Advances in nano research
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    • v.16 no.6
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    • pp.565-577
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    • 2024
  • Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. 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 Rayleigh-Ritz 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 Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

Aerodynamic noise reduction of fan motor unit of cordless vacuum cleaner by optimal designing of splitter blades for impeller (임펠라 스플리터 날개 최적 설계를 통한 무선진공청소기 팬 모터 단품의 공력 소음 저감)

  • Kim, Kunwoo;Ryu, Seo-Yoon;Cheong, Cheolung;Seo, Seongjin;Jang, Cheolmin;Seol, Hanshin
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.6
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    • pp.524-532
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    • 2020
  • In this study, noise radiated from a high-speed fan-motor unit for a cordless vacuum cleaner is reduced by designing splitter blades on the existing impeller. First of all, in order to investigate the flow field through a fan-motor unit, especially impeller, the unsteady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations are numerically solved by using computational fluid dynamic technique. With predicted flow field results as input, the Ffowcs Williams-Hawkings (FW-H) integral equation is solved to predict aerodynamic noise radiated from the impeller. The validity of the numerical methods is confirmed by comparing the predicted sound pressure spectrum with the measured one. Further analysis of the predicted flow field shows that the strong vortex is formed between the impeller blades. As the vortex induces the loss of the flow field and acts as an aerodynamic noise source, supplementary splitter blades are designed to the existing impeller to suppress the identified vortex. The length and position of splitter are selected as design factors and the effect of each design factor on aerodynamic noise is numerically analyzed by using the Taguchi method. From this results, the optimum location and length of splitter for minimum radiated noise is determined. The finally selected design shows lower noise than the existing one.