• 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.

• Journal of the Korean Society of Combustion
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• v.10 no.3
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• pp.25-33
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• 2005

Fast-time instability is investigated for diffusion flames with Lewis numbers greater than unity by employing the numerical technique called the Evans function method. Since the time and length scales are those of the inner reactive-diffusive layer, the problem is equivalent to the instability problem for the $Li\tilde{n}\acute{a}n#s$ diffusion flame regime. The instability is primarily oscillatory, as seen from complex solution branches and can emerge prior to reaching the upper turning point of the S-curve, known as the $Li\tilde{n}\acute{a}n#s$ extinction condition. Depending on the Lewis number, the instability characteristics is found to be somewhat different. Below the critical Lewis number, $L_C$, the instability possesses primarily a pulsating nature in that the two real solution branches, existing for small wave numbers, merges at a finite wave number, at which a pair of complex conjugate solution branches bifurcate. For Lewis numbers greater than $L_C$, the solution branch for small reactant leakage is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a traveling nature. As the reactant leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for L < $L_C$.

• Proceedings of the KIEE Conference
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• 2008.11b
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• pp.98-99
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• 2008

The first swing instability is the very important problem in power system operation. In this paper, the effective countermeasures to the instability. We studied the reinforcement of the transmission lines, generation tripping and reactive compensation are considered as alternative to improve transient stability.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.155-165
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• 2023

We consider circular Rayleigh problem of hydrodynamic stability which deals with linear stability of axial flows of an incompressible iniviscid homogeneous fluid to axisymmetric disturbances. For this problem, we obtained two parabolic instability regions which intersect with Batchelor and Gill semi-circle under some condition. This has been illustrated with examples. Also, we derived upper bound for the amplification factor.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.167-175
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• 2006

It has long been recognized that cancer is a genetic disease. To find this measures of genetic instability, stain cells with chromosome specific probes using chromosome in-situ hybridization technique is adopted. Even though in-situ hybridization technique is powerful, truncation of nuclei often results in under-representation of chromosome copies in slides due to the sectioning of tissue blocks. Because of this problem we suggest three different methods to analyze the cervical cancer data set. We observe that genetic instability is an increasing function of histology and our suggested model is the best in detecting genetic instability of tumorigenesis processes.

• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.103-124
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• 2013

This paper studies the static and dynamic characteristics of composite plates subjected to an arbitrary periodic load in hygrothermal environments. The material properties of composite plates are depended on the temperature and moisture. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunction transforms. A periodic load is taken to be a combination of axial pulsating load and bending stress in the example problem. The regions of dynamic instability of laminated composite plates are determined by solving the eigenvalue problems based on Bolotin's method. The effects of temperature rise and moisture concentration on the dynamic instability of laminated composite plates are investigated and discussed. The influences of various parameters on the instability region and dynamic instability index are also investigated. The numerical results reveal that the influences of hygrothermal effect on the dynamic instability of laminated plates are significant.

• Journal of ILASS-Korea
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• v.20 no.3
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• pp.168-174
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• 2015

Combustion instability is critical problem in developing liquid rocket engine. There have been many efforts to solve this problem. In this study, the method was sought through the injector as part of these efforts to suppress combustion instability. If the injector can suppress the disturbance coming from the supply line as a kind of buffer it will serve to reduce combustion instability. Especially we target at gas propellant oscillation in gas-centered swirl coaxial injector. The phenomenon is simulated with acoustic excitation of speaker. The film thickness response at injector exit was measured by using a liquid film electrode. Also the response of spray to the disturbance was observed by high-speed photography. Gas-liquid momentum flux ratio and the frequency of feeding gas oscillation were changed to investigate the effect of these experimental parameters. The trend of response by varying these parameters and the cause of weak points was studied to suggest the better design of injector for suppressing combustion instability.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.6
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• pp.295-300
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• 2003

Voltage instability has been studied for some decade now. But, There is not generally accepted definition of voltage instability because of the complex phenomenon and the variety of ways in which it can manifest itself. Both IEEE and CIGRE have the respective definitions. The areas of voltage instability research are the analysis, simulation and countermeasure of voltage instability. It needs to model the components of the power system to simulate the voltage instability and voltage collapse. At the beginning, the static simulation was used. This method provides the voltage stability indices and it requires less CPU resource and gives much insight into the voltage and power problem. However, it is less accurate than the dynamic simulation peformed in the time domain simulation. So, when it appears difficult to secure the voltage stability margin in a static stability, it is necessary to perform the dynamic simulation. To perform time-domain simulation, we have to model the dynamic component of the power system like a generator and a load. The dynamic simulation provides the accurate result of the voltage instability. But, it is not able to provide the sensitivity information or the degree of stability and it is time consuming and it needs much CPU resource. In this Paper, we perform a dynamic simulation of voltage instability and voltage collapse using EMTP MODELS. The exponential load model is designed with MODEIS and this load model is connected with test power system. The result shows the process of voltage change in time domain when the voltage instability or voltage collapse occurs.

• Journal of Power Electronics
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• v.9 no.6
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• pp.892-902
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• 2009

This paper deals with the dynamic voltage control problem at the inverter end of a HVDC link when connected to a weak AC system which has the potential for harmonic instability and commutation failures. The dynamic voltage control problem is tackled with a STATCOM (Static Compensator), which not only provides a rapid recovery from harmonic instability and commutation failures but also offers a lower cost filter design for HVDC systems. PSCAD/EMTDC simulations are presented to validate the proposed topology and to demonstrate its robust performance.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1071-1084
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• 2023

We consider inviscid, incompressible homogeneous shear flows of variable cross section known as extended Rayleigh problem. For this extended Rayleigh problem, we derived instability region which intersect with semi-circle instability region under some condition. Also we derived condition for stability, upper bound for amplification factor and growth rate of an unstable mode.