• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.663-673
• /
• 2017

We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.4
• /
• pp.518-525
• /
• 2016

This paper presents the characteristics of non-fundamental multi-mode combustion instability and the effects of high-harmonic components on the Rayleigh criterion. Phenomenological observations of multi-harmonic-mode dynamic pressure waves regarding the intensity of harmonic components and the source of wave distortion have been explained by introducing examples of second- and third-order harmonics at various amplitudes. The amplitude and order of the harmonic components distorted the wave shapes, including the peak and the amplitude, of the dynamic pressure and heat release, and consequently the temporal Rayleigh index and its integrals. A cause-and-effect analysis was used to identify the root causes of the phase delay and the amplification of the Rayleigh index. From this analysis, the skewness of the dynamic pressure turned out to be a major source in determining whether multi-mode instability is driving or damping, as well as in optimizing the combustor design, such as the mixing length and the combustor length, to avoid unstable regions. The results can be used to minimize errors in predicting combustion instability in cases of high multi-mode combustion instability. In the future, the amount of research and the number of applications will increase because new fuels, such as fast-burning syngases, are prone to generating multi-mode instabilities.

• International Journal of Aeronautical and Space Sciences
• /
• v.14 no.1
• /
• pp.19-29
• /
• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.

• Structural Engineering and Mechanics
• /
• v.22 no.4
• /
• pp.483-510
• /
• 2006

The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.17 no.1
• /
• pp.67-74
• /
• 2004

The dynamic instability for snapping phenomena has been studied by many researchers. Few paper deal with the dynamic buckling under the load with periodic characteristics, and the behavior under periodic excitation is expected the different behavior against STEP excitation. We investigate the fundamental mechanisms of the dynamic instability when the sinusoidal shaped arch structures are subjected to sinusoidal harmonic excitation with pin-ends. By using Newmark- β method, we can get the nonlinear displacement response, and using this analyze characteristics of the dynamic instability through the running response spectrum by FFT(Fast Fourier Transform).

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

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.492-497
• /
• 2003

The dynamic instability for snapping phenomena has been studied by many researches. There is few paper which deal with the dynamic buckling under the load with periodic characteristics, and the behavior under periodic excitation is expected the different behavior against STEP excitation. We investigate the fundamental mechanisms of the dynamic instability when the sinusoidal shaped arch structures subjected to sinusoidal distributed excitation with pin-ends. In this study, the dynamic direct snapping of shallow arches is investigated under not only STEP load excitation but also sinusoidal harmonic excitations, applied in the up-and-down direction. The dynamic nonlinear responses are obtained by the numerical integration of the geometrically nonlinear equations of motion, and examined by the Fourier spectral analysis in order to get the frequency-dependent characteristics of the dynamic instability for various load levels.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.2
• /
• pp.70.1-70.1
• /
• 2019

Multiple-harmonic electron cyclotron emissions, often known in the literature as the (n + 1∕2)fce emissions, are a common occurrence in the magnetosphere. These emissions are often interpreted in terms of the Bernstein mode instability driven by the electron loss cone velocity distribution function. Alternatively, they can be interpreted as quasi-thermal emission of electrostatic fluctuations in magnetized plasmas. The present paper carries out a one-dimensional relativistic electromagnetic particle-in-cell simulation and also employs a reduced quasi-linear kinetic theoretical analysis in order to compare against the simulation. It is found that the Bernstein mode instability is indeed excited by the loss cone distribution of electrons, but the saturation level of the electrostatic mode is quite low, and that the effects of instability on the electrons is rather minimal. This supports the interpretation of multiple-harmonic emission in the context of the spontaneous emission and reabsorption in quasi-thermal magnetized plasma in the magnetosphere.

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

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2003.04a
• /
• pp.69-76
• /
• 2003

We investigate the fundamental mechanisms of the dynamic instability when the sinusoidal shaped arch structures subjected to sinusoidal harmonic excitation with pin-ends. In nonlinear dynamics, examining the characteristics of attractor on the phase plane and investigating the dynamic buckling process are very important thing for understanding why unstable phenomena are sensitively originated by various initial conditions. In this study, the direct and the indirect snap-buckling of shallow arches considering geometrical nonlinearity are investigated numerically and compared with the step excitation critical load.