• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1335-1364
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• 2023

The aim of this paper is to investigate the spectral instability of roll waves bifurcating from an equilibrium in the 2-dimensional generalized Swift-Hohenberg equation. We characterize unstable Bloch wave vectors to prove that the rolls are spectrally unstable in the whole parameter region where the rolls exist, while they are Eckhaus stable in 1 dimension [13]. As compared to [18], showing that the stability of the rolls in the 2-dimensional Swift-Hohenberg equation without a quadratic nonlinearity is determined by Eckhaus and zigzag curves, our result says that the quadratic nonlinearity of the equation is the cause of such instability of the rolls.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.161-168
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• 2004

The dynamic instability of snapping phenomena has been studied by many researchers. Few papers deal with dynamic buckling under loads with periodic characteristics, and the behavior under periodic excitations is expected to be different from behavior under STEP excitations. We investigate the fundamental mechanisms of the dynamic instability when the sinusoidally shaped arch structures are subjected to sinusoidally distributed excitations with pin-ends. The mechanisms of dynamic indirect snapping of shallow arches are especially investigated under not only STEP function excitations but also under sinusoidal harmonic excitations, applied in the up-and-down direction. The dynamic nonlinear responses are obtained by the numerical integration of the geometrically nonlinear equation of motion, and examined by Fourier spectral analysis in order to get the frequency-dependent characteristics of the dynamic instability for various load levels.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.831-843
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• 2021

In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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• pp.3032-3038
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• 1994

The paper discusses a combustion instability phenomena encountered in recent solid rocket motor development efforts at ADD(Agency for Defense Development). It has happened to occur as an irregular burning in development of smokeless propellant rocket motor. Through investigating the spectral analysis of accelerometer and strain gage signals which are recorded in static firing tests and acoustic modal analysis of motor inside cavity with ANSYS, the instability is found to be the second tangential mode.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.233-235
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• 2015

This study is to investigate the combustion instability of the variation of combustion chamber length in dual swirl gas turbine model combustor. When equivalence ratio was fixed at 1.1, as the length of the combustion chamber increases the value of the frequency decreased in 7kW while the value of the frequency was constant in 4kW. The analysis of flame behaviors by high speed camera was conducted to identify such trend.

• Journal of the Korean Geophysical Society
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• v.4 no.4
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• pp.231-238
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• 2001

In this paper, an efficient LP method ofr discrete harmonic spectra is proposed and discussed. A new efficient LP method is a combination of recursive and frequency selective LP. While the recursive LP provides better spectral matching in spectral hills, frequency selective LP eliminates numerical instability and improves spectral matching when the harmonics are confined in the low frequncy region. The proposed LP method is applied to the HILN coder. Simulation results using a verification model(VM) software for real audio signals show a definite trend of significant improvement.

• The Journal of Engineering Research
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• v.5 no.1
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• pp.37-44
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• 2004

n this paper, an efficient LP method for discrete harmonic spectra is proposed and discussed. A new efficient LP method is a combination of recursive and frequency selective LP. While the recursive LP provides better spectral matching in spectral hill, frequency selective LP eliminates numerical instability and improves spectral matching when the harmonics are confined in the low frequency region. The proposed LP method is applied to the HILN coder. Simulation results using a verification model(VM) software for real audio signals show a definite trend of significant improvement.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.12
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• pp.35-40
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• 2006

The combustion instability in a model dump combustor with an exhaust nozzle and the possibility of combustion control using a loudspeaker to these instabilities were studied. By changing inlet velocity, combustor length and equivalence ratio, dynamic pressure signals and flame structures were simultaneously taken. Because inlet velocity and combustor length affect the life time of vortex in the dump combustor, the results showed that as the combustor length increased and the inlet velocity decreased, the instability frequency decreased and the maximum power spectral density of the dynamic pressure generally decreased. Also, instability frequency and maximum power spectral density of the dynamic pressure increased with the increment of equivalence ratio. From the data of close-loop control, the optimum time-delay control using a loudspeaker was confirmed to be able to reduce the vortex shedding induced from the mixed acoustic-convective mode combustion instability.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2005.11a
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• pp.445-449
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• 2005

The mixed acoustic-convective mode combustion instability and the possibility of combustion control using a loudspeaker to these instabilities were studied. By changing inlet velocity, combustor length and equivalence ratio, the dynamic pressure signals and the flame structures were simultaneously taken. The results showed that as the combustor length increased and the inlet velocity decreased, the instability frequency decreased and the maximum power spectral densities of the dynamic pressures generally decreased. The instability frequency could be affected by an equivalence ratio over the operating conditions. From the data of close-loop control, as the loudspeaker may work out-of-phase with the natural instability, the optimum time-delay controller was confirmed to be able to reduce the vortex shedding from the mixed acoustic-convective mode combustion instability.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.294-301
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• 2003

It is of often important to accurately predict the flow-induced vibration or dynamic instability of a pipeline conveying internal high speed flow in advance, which requires a very accurate solution method. In this study, first the dynamic equations for the axial and transverse vibrations of a pipeline are reduced from a set of pipe-dynamic equations derived in the previous study and then the spectral element model is formulated. The accuracy of the spectral element method (SEM) is then verified by comparing its results with the results obtained by finite element method (FEM). It is shown that the present spectral element model provides very accurate solutions by using an extremely small number of degrees-of-freedom when compared with FEM. The dynamics of a sample pipeline is investigated with varying the axial tension and the speed of internal flow.