• Nuclear Engineering and Technology
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• 제51권6호
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• pp.1650-1657
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• 2019

Fluidelastic instability and nonlinear dynamics of tube bundles is a key issue in a steam generator. Especially, once the post-instability motion of the tube becomes larger than the clearance gap to other tubes, effective contact or impact between the tubes under consideration and the other tube inevitable. There is seldom theoretical analysis to the nonlinear dynamic characteristics of a tube array in two-phase flow. In this paper, experimental and numerical studies were utilized to obtain the critical velocity of the flow-induced instability of a rotated triangular tube array. The calculation results agreed well with the experimental data. To explore the post-instability dynamics of the tube array system, a Runge-Kutta scheme was used to solve the nonlinear governing equations of tube motion. The numerical results indicated that, when the flow pitch velocity is larger than the critical velocity, the tube array system is undergoing a limit cycle motion, and the dynamic characteristics of the tube array are almost similar for different void fractions.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2003년도 제20회 춘계학술대회 논문집
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• pp.240-243
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• 2003

Combustion instability phenomena have been observed in various different combustion systems. For each specific combustion system, pressure fluctuations measured during high frequency combustion instability presented many different characteristics. High frequency instability occurring in a lean premixed gas turbine combustor mar be dominantly affected by a nonlinear relation between pressure oscillations and heat release rate fluctuations, and gas dynamics plays a crucial role in determining an amplitude of a limit cycle for a liquid rocket thrust chamber. Combustion instability phenomena manifest their inherent nonlinear characteristics. One is a limit cycle and the other bifurcation described by nonlinear time series analysis.

• International Journal of Aerospace System Engineering
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• 제2권2호
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• pp.58-61
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• 2015

Combustion instability in solid rocket motors is a long-term open problem since the first rockets were used. Based on the numerous previous studies, it is known that the limit cycle amplitude is one of the key characteristics of the nonlinear combustion instability in solid rocket motors. Flandro's extended energy balance corollary, aims to predict the limit cycle amplitude of complex, nonlinear pressure oscillations for rockets or air-breathing engines, and leads to a precise assessment of nonlinear combustion instability in solid rocket motors. However, based on the comparison with experimental data, it is revealed that the Flandro's method cannot accurately describe such a complex oscillatory pressure. Thus in this work we make modifications of the nonlinear term in the nonlinear wave equations which represents the interaction of different modes. Through this modified method, a numerical simulation of the cylindrical solid rocket has been carried out, and the simulated result consists well with the experimental data. It means that the added coefficient makes the nonlinear wave growth equations describe the experimental data better.

• Structural Engineering and Mechanics
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• 제86권6호
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• 대한수학회보
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• 제40권2호
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• pp.243-251
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• 2003

This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 2009년도 한국우주과학회보 제18권2호
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• pp.34.2-34.2
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• 2009

The relativistic Weibel instability has drawn attention as a main mechanism of the magnetic generation in the core of galaxies or in the formation of universe. The Weibel instability is not yet fully understood in the relativistic region. We investigated nonlinear saturation and decay of the relativistic Weibel instability. It is found that the early phase of the instability is in excellent agreement with the linear theory. But, an analysis based on an alternative magnetic trapping saturation theory reveals that a substantial discrepancy between the theory and simulation is revealed in the relativistic regime in contrast to an excellent agreement in the non-relativistic regime. The analysis of the Weibel instability beyond the quasilinear saturation stage shows an inverse cascade process via a nonlinear decay instability involving electrostatic fluctuation.

• Structural Engineering and Mechanics
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• 제72권4호
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• pp.525-540
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• 2019

The purpose of the present work was to study the dynamic instability of a three-layered, symmetric sandwich beam subjected to a periodic axial load resting on nonlinear elastic foundation. A higher-order theory was used for analysis of sandwich beams with soft core on elastic foundations. In the higher-order theory, the Reddy's third-order theory was used for the face sheets and quadratic and cubic functions were assumed for transverse and in-plane displacements of the core, respectively. The elastic foundation was modeled as nonlinear's type. The dynamic instability regions and free vibration were investigated for simply supported conditions by Bolotin's method. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the coefficients of foundation, the core thickness, the dynamic and static load factor. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.

• 한국추진공학회지
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• 제16권6호
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• pp.41-47
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• 2012

연소 불안정 현상을 완전하게 이해하기 위해서는 천이 과정과 한계 진폭과 같은 비선형 거동에 대한 예측이 매우 중요하다. 가스터빈 희박 예혼합 연소기에서 이러한 비선형 거동은 화염의 비선형 동특성에 크게 의존하게 된다. 본 연구에서는 기존에 선형 해석으로부터 비선형 열음향 해석으로 확장하기 위해서 화염 묘사 함수를 통한 시스템 안정성 해석 기법이 소개되었다. 이를 위하여, 주파수 뿐만 아니라 속도 진폭에 따른 열발생율의 변동 특성이 실험 결과로부터 모델링되었다. 현재 해석 조건에서 비선형 모델링 결과, 주어진 연소기 길이에서 속도 진폭이 불안정 주파수에 미치는 영향은 미비하였으나, 성장률에는 크게 영향을 미치는 것으로 나타났다. 향후 다양한 조건에서 비선형 모델의 검증과 한계 진폭의 예측 결과에 대한 실험 결과와의 비교가 요구된다.

• 한국공간구조학회논문집
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• 제10권2호
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• pp.95-103
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• 2010

본 논문에서는 비선형 강성방정식의 정확성 향상에 관해 연구한다. 대공간 구조물은 대경간을 가볍게 만들기 위해 두께비를 얇게 만들어야 하므로, 구조설계시 구조불안정 검토가 중요하다. 쉘형 구조물의 구조불안정은 초기 조건에 매우 민감하게 반응하며, 이는 대변형을 수반하는 비선형 문제에 귀착하게 된다. 따라서 구조불안정을 정확히 알아보기 위해 비선형 강성방정식의 정확성이 향상 되어야 한다. 본 연구에서는 스페이스 트러스를 해석 모델로 하며 접선 강성방정식과 비선형 강성방정식의 두 이론을 프로그램으로 작성하여 비선형 해석을 수행한다. 두 이론의 해석 결과를 비교 고찰하여 비선형 강성방정식의 정확성 및 수렴성 향상에 대해 검토 한다.

• Coupled systems mechanics
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• 제3권1호
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• pp.89-110
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• 2014

In this work we provide the theoretical formulation, discrete approximation and solution algorithm for instability problems combing geometric instability at large displacements and material instability due to softening under combined thermo-mechanical extreme loads. While the proposed approach and its implementation are sufficiently general to apply to vast majority of structural mechanics models, more detailed developments are provided for truss-bar model. Several numerical simulations are presented in order to illustrate a very satisfying performance of the proposed methodology.