• Title/Summary/Keyword: Energy Integral

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A Study on the Nonlinear Normal Mode Vibration Using Adelphic Integral (Adelphic Integral을 이용한 비선형 정규모드 진동 해석)

  • Huinam Rhee;Joo, Jae-Man;Pak, Chol-Hui
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.11b
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    • pp.799-804
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    • 2001
  • Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

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Non-linear analysis of dealamination fracture in functionally graded beams

  • Rizov, Victor I.
    • Coupled systems mechanics
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    • v.6 no.1
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    • pp.97-111
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    • 2017
  • The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

Analysis of Time-Varying Linear System Using the New Integral Operational Matrix via Block Pulse Functions (블록펄스 함수의 새로운 적분연산 행렬을 이용한 선형 시변계의 해석)

  • Cho, Young-Ho;Shin, Seung-Kwon;Park, Jung-Ho;Lee, Han-Seok;Kim, Jae-Il;Ahn, Doo-Soo
    • Proceedings of the KIEE Conference
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    • 1999.07b
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    • pp.755-757
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    • 1999
  • The operational properties of BPF(block-pulse functions) are much applied to the analysis of time-varying linear systems. The integral operational matrix of BPF converts the systems in the form of the differential equation into the algebraic problems. But the errors caused by using the integral operational matrix make it difficult that we exactly analyze time-varying linear systems. So, in this paper, to analyze time-varying linear systems we had used the recursive algorithm derived from the new integral operational matrix. And the usefulness of the proposed method is verified by the example.

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On the Modification of Gauss Integral Point of 6 Node Two Dimensional Isoparametric Element -Linear and Nonlinear Static and Dynamic Bending Analyses- (6절점 2차원 Isoparametric요소의 가우스적분점 수정에 관하여 -선형, 비선형의 정적 및 동적 굽힘해석-)

  • 김정운;정래훈;권영두
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.12
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    • pp.3007-3019
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    • 1993
  • For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

A Study on Energy Release Rate for Interface Cracks in Anisotropic Dissimilar Materials (이방성 이종재 접합계면 균열의 에너지 해방률에 관한 연구)

  • Kim, Jin-Gwang;Jo, Sang-Bong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.11
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    • pp.1835-1843
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    • 2001
  • The energy release rate for an interface crack in anisotropic dissimilar materials was obtained by the eigenfunction expansion method and also was analyzed numerically by the reciprocal work contour integral method. It was shown that the results for orthotropic dissimilar materials are consistent with the other worker's results.

Coriolis Coupling Influence on the H+LiH Reaction

  • Zhai, Hongsheng;Li, Wenliang;Liu, Yufang
    • Bulletin of the Korean Chemical Society
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    • v.35 no.1
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    • pp.151-157
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    • 2014
  • We have reported the reaction probability, integral reaction cross section, and rate constant for the title system calculated with the aid of a time-dependent wave packet approach. The ab initio potential energy surface (PES) of Prudente et al. (Chem. Phys. Lett. 2009, 474, 18) is employed for the purpose. The calculations are carried out over the collision energy range of 0.05-1.4 eV for the two reaction channels of H + LiH ${\rightarrow}$ Li + $H_2$ and $H_b$ + $LiH_a$ ${\rightarrow}$ $LiH_b$ + $H_a$. The Coriolis coupling (CC) effect are taken into account. The importance of including the Coriolis coupling quantum scattering calculations are revealed by the comparison between the Coriolis coupling and the centrifugal sudden (CS) approximation calculations.

An Analysis of Fast Critical Experiments Using JEF-1-Based 50-Group Constant Set (JEF-1의 50군 단면적에 의한 고속 임계실험 해석)

  • Kim, Jung-Do;Gil, Choong-Sup;Kim, Young-Cheol
    • Nuclear Engineering and Technology
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    • v.25 no.3
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    • pp.457-469
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    • 1993
  • JEF-1-based 50-group cross section set for fast reactor calculations was generated using NJOY system. The set was then examined by analyzing measured integral quantities such as criticality and central reaction rate ratios for 27 fast critical assemblies. The calculated results using the new set were also compared with those of ENDF/B-IV or-V-based fast set. In general, the JEF-1-based set shows an improvement in predicting measured integral quantities in comparison with the previous set. With a few exceptions, JEF-1 results are comparable to those of ENDF/B-V.

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LBLOCA AND DVI LINE BREAK TESTS WITH THE ATLAS INTEGRAL FACILITY

  • Baek, Won-Pil;Kim, Yeon-Sik;Choi, Ki-Yong
    • Nuclear Engineering and Technology
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    • v.41 no.6
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    • pp.775-784
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    • 2009
  • This paper summarizes the tests performed in the ATLAS facility during its first two years of operation (2007${\sim}$2008). Two categories of tests have been performed successfully: (a) the reflood phase of the large-break loss-of-coolant accidents in a cold leg, and (b) the breaks in one of four direct vessel injection lines. Those tests contributed to understanding the unique thermal-hydraulic behavior, resolving the safety-related concerns and providing an evaluation of the safety analysis codes and methodology for the advanced pressurized water reactor, APR1400. Several important and interesting phenomena have been observed during the tests. In most cases, the ATLAS shows reasonable accident characteristics and conservative results compared with those predicted by one-dimensional safety analysis codes. A wide variety of small-break LOCA tests will be performed in 2009.