• Title/Summary/Keyword: Nonlinear Superposition

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Nonlinear Tidal Characteristics along the Uldolmok Waterway off the Southwestern Tip of the Korean Peninsula

  • Kang, Sok-Kuh;Yum, Ki-Dai;So, Jae-Kwi;Song, Won-Oh
    • Ocean and Polar Research
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    • v.25 no.1
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    • pp.89-106
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    • 2003
  • Analyses of tidal observations and a numerical model of the $M_2$ and $M_4$ tides in the Uldolmok waterway located at the southwestern tip of the Korean Peninsula are described. This waterway is well known fer its strong tidal flows of up to more than 10 knots at the narrowest part of the channel. Harmonic analysis of the observed water level at five tidal stations reveals dramatic changes in the amplitude and phase of the shallow water constituents at the station near the narrowest part, while survey results show a decreasing trend in local mean sea levels toward the narrow section. It was also observed that the amplitudes of semi-diurnal constituents, $M_2$ and $S_2$ are diminishing toward the narrowest part of the waterway. Two-dimensional numerical modeling shows that the $M_2$ energy flux is dominated by the component coming from the eastern boundary. The $M_2$ energy is inward from both open boundaries and is transported toward the narrow region of the channel, where it is frictionally dissipated or transferred to other constituents due to a strong non-linear advection effect. It is also shown that the $M_4$ generation is strong around the narrow region, and the abrupt decrease in the M4 amplitude in the region is due to a cancellation of the locally generated M4 with the component propagated from open boundaries. The superposition of both propagated and generated M4 contributions also explains the discontinuity of the M4 phase lag in the region. The tide-induced residual sea level change and the regeneration effect of the $M_2$ tide through interaction with $M_4$ are also examined.

Fatigue Design of Spot Welded Lap Joint Considered Residual Stress (잔류응력을 고려한 점용접이음재의 피로설계)

  • Son, Il-Seon;Bae, Dong-Ho;Hong, Jeong-Gyun;Lee, Beom-No
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.3 s.174
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    • pp.743-751
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    • 2000
  • Because welding residual stress is formidable result in electric resistance spot welding process, and it detrimentally affect to fatigue crack initiation and growth at nugget edge of spot welded la p joints, it should be considered in fatigue analysis. Thus, accurate prediction of residual stress is very important. In this study, nonlinear finite element analysis on welding residual stress generated in process of the spot welding was conducted, and their results were compared with experimental data measured by X-ray diffraction method. By using their results, the maximum principal stress considered welding residual stress at nugget edge of the spot welded lap joint subjected to tension-shear load was calculated by superposition method. And, the $\Delta$P- $N_f$ relations obtained through fatigue, tests on the IB-type spot welded lap joints was systematically rearranged with the maximum principal stress considered welding residual stress. From the results, it was found th2at fatigue strength of the IB-type spot welded lap joints could be systematically and more reasonably rearranged by the maximum principal stress($\sigma$1max-res considered welding residual stress at nugget edge of the spot welding point.

Analysis of Multi-Layered Structural Systems Using Nonlinear Finite Elements-Boundary Elements (반무한 다중 구조계의 비선형 유한요소 - 경계요소 해석)

  • 김문겸;장정범;이상도;황학주
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1992.04a
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    • pp.58-64
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    • 1992
  • It is usual that underground structures are constructed within multi-layered medium. In this paper, an efficient numerical model ling of multi-layered structural systems is studied using coupled analysis of finite elements and boundary elements. The finite elements are applied to the area in which the material nonlinearity is dominated, and the boundary elements are applied to the far field area where the nonlinearity is relatively weak. In the boundary element model 1 ins of the multi-layered medium, fundamental solutions are restricted. Thus, methods which can utilize existing Kelvin and Melan solution are sought for the interior multi-layered domain problem and semi infinite domain problem. Interior domain problem which has piecewise homogeneous layers is analyzed using boundary elements with Kelvin solution; by discretizing each homogeneous subregion and applying compatibility and equilibrium conditions between interfaces. Semi-infinite domain problem is analyzed using boundary elements with Melan solution, by superposing unit stiffness matrices which are obtained for each layer by enemy method. Each methodology is verified by comparing its results which the results from the finite element analysis and it is concluded that coupled analysis using boundary elements and finite elements can be reasonable and efficient if the superposition technique is applied for the multi-layered semi-infinite domain problems.

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Developement and application of Statistical Hydrofracturing Data Processing Program (통계적 접근법에 의한 수압파쇄 자료해석용 전산 프로그램 개발 및 적용)

  • 류동우;최성웅;이희근
    • Tunnel and Underground Space
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    • v.6 no.3
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    • pp.209-222
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    • 1996
  • Shut-in pressure, reopenting pressure and fracture orientation are very important parameters to be evaluated precisely in in-situ stress measurement by hydraulic fracturing. Graphical methods on pressure-time curves have been conventionally used, even though these are seriously dependent on subjectivity of interpreters. So there have been many demands on new method to objectivity in determining parameters. We have developed integrated hydrofracturing data processing program (HYDFRAC), based on nonlinear regression analysis and can be invoked under the Window graphical user interface. HYDFRAC consiste of three routines, that is shut-in pressure routine, reopening pressure routine, and fracture delineation routine. Each of routines include independent modules according to parameter determination methods. Its application to field tests ensured both objectivity and facility in determining of hydraulic fracturing parameters. Determining shut-in pressures at each pressurization cycles, we adopted the exponential pressure-decay method(EPD method), the bilinear pressure-decay-rate method (PDR method), and the tangent intersection method in order to find the pressurization-cyclic tendency of shut-in pressures. The estimated pressure by PDR method exists in the range of the upper and lower values by EPD method, and lies near to the upper value more than the lower. Being the pressurization cycle increased, the range of upper and lower limits come to be stabilized gradually. By graphical superposition method and bilinear pressure-accumulated volume method, reopening pressures were determined. Vertical and inclined fracture attitudes were determined by applying the directional statistics and sinusoidal curve fitting, respectively. The results of evaluation of hydrofracturing parameters showed that statistical methods could enhance the objectivity better than graphical methods.

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Dynamic characteristics of elastic beams subjected to traffic loads

  • Tang, Chia-Chih;Wang, Yang-Cheng
    • Structural Engineering and Mechanics
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    • v.13 no.2
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    • pp.211-230
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    • 2002
  • The objective of this study is to investigate the dynamic behavior of elastic beams subjected to moving loads. Although analytical methods are available, they have limitations with respect to complicated structures. The use of computer technology in recent years is an effective way to solve the problem; thus using the latest technology this study establishes a finite-element solution procedure to investigate dynamic behaviors of a typical elastic beam having a set of constant geometric properties and various span lengths. Both the dead load of the beam and traffic load are applied in which the traffic load is considered a concentrated moving force with various traveling passage speeds on the beam. Dynamic behaviors including deflection, shear, and bending moment due to moving loads are obtained by both analytical and finite element methods; for simple structures, they have an excellent agreement. The numerical results show that based on analytical methods the fundamental mode is good enough to estimate the dynamic deflection along the beam, but is not sufficient to simulate the total response of the shear force or the bending moment. The linear dynamic behavior of the elastic beams subjected to multiple exciting loads can easily be found by linear superposition, and the geometric nonlinear results caused by large deformation and axial force of the beam are always underestimated with only a few exceptions which are indicated. In order to make the results useful, they have been nondimensionalized and presented in graphical form.

Applied Koopmanistic interpretation of subcritical prism wake physics using the dynamic mode decomposition

  • Cruz Y. Li;Xisheng Lin;Gang Hu;Lei Zhou;Tim K.T. Tse;Yunfei Fu
    • Wind and Structures
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    • v.37 no.3
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    • pp.191-209
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    • 2023
  • This work investigates the subcritical free-shear prism wake at Re=22,000 by the Koopman analysis using the Dynamic Mode Decomposition (DMD) algorithm. The Koopman model linearized nonlinearities in the stochastic, homogeneous anisotropic turbulent wake, generating temporally orthogonal eigen tuples that carry meaningful, coherent structures. Phenomenological analysis of dominant modes revealed their physical interpretations: Mode 1 renders the mean-field dynamics, Modes 2 describes the roll-up of the Strouhal vortex, Mode 3 describes the Bloor-Gerrard vortex resulting from the Kelvin-Helmholtz instability inside shear layers, its superposition onto the Strouhal vortex, and the concurrent flow entrainment, Modes 6 and 10 describe the low-frequency shedding of turbulent separation bubbles (TSBs) and turbulence production, respectively, which contribute to the beating phenomenon in the lift time history and the flapping motion of shear layers, Modes 4, 5, 7, 8, and 9 are the relatively trivial harmonic excitations. This work demonstrates the Koopman analysis' ability to provide insights into free-shear flows. Its success in subcritical turbulence also serves as an excellent reference for applications in other nonlinear, stochastic systems.

Parametric Array Signal Generating System using Transducer Array (트랜스듀서 배열을 이용한 파라메트릭 배열 신호 생성 시스템)

  • Lee, Jaeil;Lee, Chong Hyun;Bae, Jinho;Paeng, Dong-Guk;Choe, Mi Heung;Kim, Won-Ho
    • The Journal of the Acoustical Society of Korea
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    • v.32 no.4
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    • pp.287-293
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    • 2013
  • We present a parametric array signal generating system using $3{\times}16$ transducer array which is composed of multi-resonant frequency transducers of 20kHz and 32.5kHz. To drive transducer array, sixteen channel amplifier using LM1875 chips is designed and implemented, and the PXI system based on the LabView 8.6 for arbitrary signal generation and analysis is used. Using the proposed system, we measure sound pressure level and beam pattern of difference frequency and verify the nonlinear effect of difference frequency. The theoretical absorption range and the Rayleigh distance are 15.51m and 1.933m, respectively and we verify that sound pressure of difference frequency is accumulated and increased at the near-field shorter than the Rayleigh distance. We verify that the beam pattern of the measured difference frequency and the beam pattern obtained by the superposition of two primary frequencies are similar, and high directional parametric signal was generated.

Nonlinear Behavior Analysis of RC Shear Wall Using Truss Theory (트러스 이론을 이용한 철근 콘크리트 전단벽의 비선형 거동해석)

  • Seo, Soo-Yeon;Kim, Jeong-Sik;Choi, Yun-Chul;Lee, Li-Hyung
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.9 no.3
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    • pp.213-220
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    • 2005
  • Recently, a concern to verify the displacement capacity of shear wall has been arised to produce suitable data for the performance based design. In this paper, a process is presented to evaluate the displacement capacity of shear wall. The displacement of shear wall is expressed as the superposition of shear and flexural deformation. Variable crack angle truss model with a modification and sectional analysis method are used in calculating shear and flexural displacement, respectively. In addition, the effect of axial force and the contribution of vertical and horizontal reinforcements in wall are considered in the analysis. The accuracy of proposed method is evaluated by the comparison calculation results with previous test results. From the comparison, it was shown that the hysteretic behavior of shear wall could be well predicted by using the process. In the case with flange wall, however, the method overestimates the contribution of flange wall for strength and stiffness and underestimates for displacement capacity.

Development of a Fatigue Damage Model of Wideband Process using an Artificial Neural Network (인공 신경망을 이용한 광대역 과정의 피로 손상 모델 개발)

  • Kim, Hosoung;Ahn, In-Gyu;Kim, Yooil
    • Journal of the Society of Naval Architects of Korea
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    • v.52 no.1
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    • pp.88-95
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    • 2015
  • For the frequency-domain spectral fatigue analysis, the probability density function of stress range needs to be estimated based on the stress spectrum only, which is a frequency domain representation of the response. The probability distribution of the stress range of the narrow-band spectrum is known to follow the Rayleigh distribution, however the PDF of wide-band spectrum is difficult to define with clarity due to the complicated fluctuation pattern of spectrum. In this paper, efforts have been made to figure out the links between the probability density function of stress range to the structural response of wide-band Gaussian random process. An artificial neural network scheme, known as one of the most powerful system identification methods, was used to identify the multivariate functional relationship between the idealized wide-band spectrums and resulting probability density functions. To achieve this, the spectrums were idealized as a superposition of two triangles with arbitrary location, height and width, targeting to comprise wide-band spectrum, and the probability density functions were represented by the linear combination of equally spaced Gaussian basis functions. To train the network under supervision, varieties of different wide-band spectrums were assumed and the converged probability density function of the stress range was derived using the rainflow counting method and all these data sets were fed into the three layer perceptron model. This nonlinear least square problem was solved using Levenberg-Marquardt algorithm with regularization term included. It was proven that the network trained using the given data set could reproduce the probability density function of arbitrary wide-band spectrum of two triangles with great success.

Error Rate Performance of DS-BPSK Signal transmitted through a Hard-Limiting Satellite Channel in the presence of Interference and Noise (간섭과 잡음이 존재하는 Hard-Limiting 위성채널상에서의 DS-BPSK신호의 오율특성)

  • 신동일;조성준
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.11 no.1
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    • pp.64-72
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    • 1986
  • The error rate equation fo DS-BPSK(Direct Sequence Binary Phase Shift Keying) signal transmitted through the nonlinear satellite transponder has been derived in the cochannel interference and downlink Gaussian noise environment. The input to the satellite transponder is the superposition of DS-BPSK signal with one interfere which is a cochannel wide-band PN signal. The error rate performance of DS-BPSK system has been evaluated and shown in figures in terms of carrier to interference power ratio(CIR), downlink signal to noise power ratio(downlink SNR) and process gain. In the analysis, it has been shown that the use of a hard limiter in DS-BPSK satellite system leads to the generation of narrow-band intermodulation products which is independent of the process gain. Also it is known that the error rate performance can be improved in the low levels (below 10dB) of CIR as the CIR increase. As the process gain varies from 10 to 100 the curve gives the about 10 dB gain in downlink SNR to maintain a fixed error rate.

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