• Title/Summary/Keyword: Bifurcation Modes

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Buckling Analysis of the Large Span Spatial Structures by Modal Analysis (Modal Analysis법에 의한 무주대공간 구조물의 좌굴해석)

  • 한상을;권택진
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1996.10a
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    • pp.195-201
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    • 1996
  • This paper is mainly forcused on the application of modal analysis In analyze the geometrically non-linear buckling behaviors of large span spatial structures, and the evaluation of each eigen mode affected post-buckling behaviors and buckling loads. Modal analysis is applied . to derivation of the system matrices transforming actual displacement space into generalized coordinates space represented by coefficients multiplied in the linear combination of eigen modes which are independent and orthogonal each other. By using modal analysis method, it will be expected to save the calculating time by computer extremely. For example, we can obtain the satisfactorily good results by using about 7% of total eigen modes only in case of single layer latticed dome. And we can decrease the possibility of divergence on the bifurcation point in the calculation of post-buckling path. Arc-length method and Newton-Raphson iteration method are used to calculate the nonlinear equilibrium path.

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Hyperbolic Reaction-Diffusion Equation for a Reversible Brusselator: Solution by a Spectral Method

  • 이일희;김광연;조웅인
    • Bulletin of the Korean Chemical Society
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    • v.20 no.1
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    • pp.35-41
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    • 1999
  • Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

Research on Numerical Calculation of Normal Modes in Nonlinear Vibrating Systems (비선형 진동계 정규모드의 수치적 계산 연구)

  • Lee, Kyoung-Hyun;Han, Hyung-Suk;Park, Sungho;Jeon, Soohong
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.26 no.7
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    • pp.795-805
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    • 2016
  • Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

On the Normal Mode Dynamics of a Pendulum Absorber (정규모우드 방법을 활용한 진자형 흡진기의 비선형 동역학에 관한 연구)

  • 심재구;박철희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1996.04a
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    • pp.177-183
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    • 1996
  • By utilizing the concept of normal modes, nonlinear dynamics is studied on pendulum dynamic absorber. When the spring mode loses the stability in undamped free system, a dynamic two-well potential is formed in Poincare map. A procedure is formulated to compute the forced responses associated with bifurcating mode and predict double saddle-loop phenomenon. It is found that quasiperiodic motion and stable periodic motion coexist in some parameter ranges, and only periodic motions or rotation of pendulum with chaotic fluctuation are observed in other ranges.

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Monte Carlo Simulation of Thermionic Low Pressure Discharge Plasma (저압 열전자 방전 플라즈마의 Monte Carlo 시뮬레이션)

  • Koh, Wook Hee
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.12
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    • pp.1880-1885
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    • 2012
  • Nonlinear dynamical behaviors in thermionic low pressure discharge are investigated using a particle-in-cell(PIC) simulation. An electrostatic PIC code is developed to model the plasma discharge system including the kinetic effects. The elastic collision, excitation collision, ionization collision, and electron-ion recombination collision are considered in this code. The generated electrons and ions are traced to analyze physical characteristics of the plasma. The simulation results show that the nonlinear oscillation structures are observed for cold plasma in the system and the similar structures are observed for warm plasma with a shift in values of the bifurcation parameter. The detailed oscillation process can be subdivided into three distinct mode; anode-glow, temperature-limited, and double-layer modes.

Internal resonance and nonlinear response of an axially moving beam: two numerical techniques

  • Ghayesh, Mergen H.;Amabili, Marco
    • Coupled systems mechanics
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    • v.1 no.3
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    • pp.235-245
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    • 2012
  • The nonlinear resonant response of an axially moving beam is investigated in this paper via two different numerical techniques: the pseudo-arclength continuation technique and direct time integration. In particular, the response is examined for the system in the neighborhood of a three-to-one internal resonance between the first two modes as well as for the case where it is not. The equation of motion is reduced into a set of nonlinear ordinary differential equation via the Galerkin technique. This set is solved using the pseudo-arclength continuation technique and the results are confirmed through use of direct time integration. Vibration characteristics of the system are presented in the form of frequency-response curves, time histories, phase-plane diagrams, and fast Fourier transforms (FFTs).

Investigation of Self-Excited Combustion Instabilities in Two Different Combustion Systems

  • Seo, Seonghyeon
    • Journal of Mechanical Science and Technology
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    • v.18 no.7
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    • pp.1246-1257
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    • 2004
  • The objective of this paper is to characterize dynamic pressure traces measured at self-excited combustion instabilities occurring in two combustion systems of different hardware. One system is a model lean premixed gas turbine combustor and the other a fullscale bipropellant liquid rocket thrust chamber. It is commonly observed in both systems that low frequency waves at around 300㎐ are first excited at the onset of combustion instabilities and after a short duration, the instability mode becomes coupled to the resonant acoustic modes of the combustion chamber, the first longitudinal mode for the lean premixed combustor and the first tangential mode for the rocket thrust chamber. Low frequency waves seem to get excited at first since flame shows the higher heat release response on the lower frequency perturbations with the smaller phase differences between heat release and pressure fluctuations. Nonlinear time series analysis of pressure traces reveals that even stable combustion might have chaotic behavior with the positive maximum Lyapunov exponent. Also, pressure fluctuations under combustion instabilities reach a limit cycle or quasi-periodic oscillations at the very similar run conditions, which manifest that a self-excited high frequency instability has strong nonlinear characteristics.

Secondary buckling analysis of spherical caps

  • Kato, Shiro;Chiba, Yoshinao;Mutoh, Itaru
    • Structural Engineering and Mechanics
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    • v.5 no.6
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    • pp.715-728
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    • 1997
  • The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter's shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.

Resisting Strength of Ring-Stiffened Cylindrical Steel Shell under Uniform External Pressure (균일외압을 받는 링보강 원형단면 강재 쉘의 강도특성)

  • Ahn, Joon Tae;Shin, Dong Ku
    • Journal of Korean Society of Steel Construction
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    • v.30 no.1
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    • pp.25-35
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    • 2018
  • Resisting strength of ring-stiffened cylindrical steel shell under uniform external pressure was evaluated by geometrically and materially nonlinear finite element method. The effects of shape and amplitude of geometric initial imperfection, radius to thickness ratio, and spacing of ring stiffeners on the resisting strength of ring-stiffened shell were analyzed. The resisting strength of ring-stiffened cylindrical shells made of SM490 obtained by FEA were compared with design strengths specified in Eurocode 3 and DNV-RP-C202. The shell buckling modes obtained from a linear elastic bifurcation FE analysis were introduced in the nonlinear FE analysis as initial geometric imperfections. The radius to thickness ratios of cylindrical shell in the range of 250 to 500 were considered.

A Study of Unstable Phenomenon of Flow Truss Dome Structure with Asymmetric Load Modes (Flow Truss Dome 구조물의 비대칭 하중모드에 따른 불안정 현상에 관한 연구)

  • Shon, Su-Deok;Kim, Seung-Deog;Kang, Moon-Myung
    • Journal of Korean Association for Spatial Structures
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    • v.2 no.4 s.6
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    • pp.61-76
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    • 2002
  • The structure system that is discreterized by continuous shells is usually used to make a large space structures and these structures show the collapse mechanisms that are captured at over the limit load, and snap-through and bifurcation are most well known of it. For the collapse mechanism, rise-span ratio, element stiffness and load mode are main factor, which it give an effect to unstable behavior. Moreover, resist force of structure can be reduced by initial condition and initial imperfection significantly. In order to investigate the instability of shell structures, the finite deformation theory can be applied and it becomes a nonlinear mathematics in which use equation of tangential stiffness incrementally. With an initial imperfection, using simple example and Flow Truss Dome, the buckling characteristics of space truss is main purpose of this paper, and unstable behavior is studied by proposed the numerical method. Also, by using MIDAS, this research work analyzes displacements and inner forces as the design load of model, and the ratio of buckling load of design load is investigated.

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