• Journal of ILASS-Korea
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• v.2 no.1
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• pp.8-17
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• 1997

A study has been carried out on the instability of a conical liquid sheet by using the linear instability theory. Various analytical methods using the Kelvin-Helmholtz instability theory were tried to examine the wave growth on cylindrical liquid sheets. Cylinderical liquid sheets were extended to the case with the conical sheets. Perturbations due to tangential motion as well as longitudinal one were taken into account. And it was assumed the the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. The predicted drop size agreed well with the measured Sauter mean diameter, $D_{32}$.

• Wind and Structures
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• v.26 no.6
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• pp.355-367
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• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Journal of the Korean Society of Combustion
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• v.7 no.1
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• pp.23-30
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• 2002

Instability of oblique detonation waves (ODW) at off-attaching condition was investigated through a series of numerical simulations. Two-dimensional wedge of finite length was considered in $H_2/O_2/N_2$ mixtures at superdetonative condition. Numerical simulation was carried out with a compressible fluid dynamics code and a detailed hydrogen-oxygen combustion mechanism. Present result reveals that there is a chemical kinetic limit of the ODW detachment, in addition to the theoretical limit predicted by Rankine-Hugoniot theory with equilibrium chemistry. Result also presents that ODW still attaches at a wedge as an oblique shock-induced flame showing periodically unstable motion, if the Rankine-Hugoniot limit of detachment is satisfied but the chemical kinetic limit is not. Mechanism of the periodic instability is considered as interactions of shock and reaction waves coupled with chemical kinetic effects. From the investigation of characteristic chemical time, condition of the periodic instability is identified as follows; at the detaching condition of the Rankine-Hugoniot theory, (1) flow residence time is smaller than the chemical characteristic time, behind the detached shock wave with heat addition, (2) flow residence time should be greater than the chemical characteristic time, behind an oblique shock wave without heat addition.

• Bulletin of the Korean Chemical Society
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• v.8 no.3
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• pp.196-200
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• 1987

A nonlinear theory presented previously is applied to the Oregonator, which is a model for the Belousov-Zhabotinskii reaction, to study instability near the critical point driven by diffusions. The result shows that the theory may be applied to an actual system.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.401-413
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• 2011

The aerodynamic stability of orthotropic tensioned membrane structures with rectangular plane is theoretically studied under the uniform ideal potential flow. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. Then, based on the large amplitude theory and the D'Alembert's principle, the interaction governing equation of wind-structure is established. Under the circumstances of single mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second order nonlinear differential equation with constant coefficients. Through judging the stability of the system characteristic equation, the critical divergence instability wind velocity is determined. Finally, from different parametric analysis, we can conclude that it has positive significance to consider the characteristics of orthotropic and large amplitude for preventing the instability destruction of structures.

• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• International Journal of Fluid Machinery and Systems
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• v.4 no.1
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• pp.114-132
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• 2011

We have proposed a new approach based on energy gradient concept for the study of flow instability and turbulent transition in parallel flows in our previous works. It was shown that the disturbance amplitude required for turbulent transition is inversely proportional to Re, which is in agreement with the experiments for imposed transverse disturbance. In present study, the energy gradient theory is extended to the generalized curved flows which have much application in turbomachinery and other fluid delivery devices. Within the frame of the new theory, basic theorems for flow instability in general cases are provided in details. Examples of applications of the theory are given from our previous studies which show comparison of the theory with available experimental data. It is shown that excellent agreement has been achieved for several configurations. Finally, various prediction methods for turbulent transition are reviewed and commented.

• Wind and Structures
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• v.25 no.5
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• pp.415-432
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• 2017

The nonlinear aerodynamic instability of a tensioned plane orthotropic membrane structure is theoretically investigated in this paper. The interaction governing equation of wind-structure coupling is established by the Von $K\acute{a}rm\acute{a}n's$ large amplitude theory and the D'Alembert's principle. The aerodynamic force is determined by the potential flow theory of fluid mechanics and the thin airfoil theory of aerodynamics. Then the interaction governing equation is transformed into a second order nonlinear differential equation with constant coefficients by the Bubnov-Galerkin method. The critical wind velocity is obtained by judging the stability of the second order nonlinear differential equation. From the analysis of examples, we can conclude that it's of great significance to consider the orthotropy and geometrical nonlinearity to prevent the aerodynamic instability of plane membrane structures; we should comprehensively consider the effects of various factors on the design of plane membrane structures; and the formula of critical wind velocity obtained in this paper provides a more accurate theoretical solution for the aerodynamic stability of the plane membrane structures than the previous studies.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.47.2-47.2
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• 2016

The protons and helium ions in the solar wind are observed to possess anisotropic temperature profiles. The anisotropy appears to be limited by various marginal instability conditions. One of the efficient methods to investigate the global dynamics and distribution of various temperature anisotropies in the large-scale solar wind models may be that based upon the macroscopic quasi-linear approach. The present paper investigates the proton and helium ion anisotropy instabilities on the basis of comparison between the quasi-linear theory versus particle-in-cell simulation. It is found that the overall dynamical development of the particle temperatures is quite accurately reproduced by the macroscopic quasi-linear scheme. The wave energy development in time, however, shows somewhat less restrictive comparisons, indicating that while the quasi-linear method is acceptable for the particle dynamics, the wave analysis probably requires higher-order physics, such as wave-wave coupling or nonlinear wave-particle interaction. We carried out comparative studies of proton firehose instability, aperiodic ordinary mode instability, and helium ion anisotropy instability. It was found that the agreement between QL theory and PIC simulation is rather good. It means that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.14-17
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• 1999

The wrinkling behavior of a thin sheet with perfect geometry is a kind of compressive instability. The compressive instability is influenced by many factors such as stress state mechanical properties of the sheet material geometry of the body contact conditions and plastic anisotropy. The analysis of compressive instability in plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show wide variation for small deviation of the factors. In this study the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. in order to investigate the effect of plastic anisotropy on the compressive instability a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentionedfinite element analysis. The critical stress ratios above which the buckling does not take place are found for various plastic anisotropic modeling method and discussed. Finally the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated.