• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.45-52
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• 2008

In order to investigate the initiation and propagation processes of a spherical detonation wave induced by direct initiation, numerical simulations were carried out using two-dimensional compressible Euler equations with an axisymmetric assumption and a one-step reaction model based on Arrhenius kinetics with various levels of ignition energy. By varying the amount of ignition energy, three typical initiation behaviors, which were subcritical, supercritical and critical regimes, were observed. Then, the ignition energy of more than $137.5{\times}10^6$ in non-dimensional value was required for initiating a spherical detonation wave, and the minimum ignition energy(i.e., critical energy) was less than that of the one-dimensional simulation reported by a previous numerical work. When the ignition energy was less than the critical energy, the blast wave generated from an ignition source continued to attenuate due to the separation of the blast wave and a reaction front. Therefore, detonation was not initiated in the subcrtical regime. When the ignition energy was more than the minimum initiation energy, the blast wave developed into a multiheaded detonation wave propagating spherically at CJ velocity, and then a cellular pattern radiated regularly out from the ignition center in the supercritical regime. The influence on ignition energy was observed in the cell width near the ignition center, but the cell width on the fully developed detonation remained constant during the expanding of detonation wave due to the consecutive formation of new triple points, regardless of ignition energy. When the ignition energy was equal to the critical energy, the decoupling of the blast wave and a reaction front appeared, as occurred in the subcrtical regime. After that, the detonation bubble induced by the local explosion behind the blast wave expanded and developed into the multiheaded detonation wave in the critical regime. Although few triple points were observed in the vicinity of the ignition core, the regularly located cellular pattern was generated after the onset of the multiheaded detonation. Then, the average cell width on the fully developed detonation was almost to that in the supercritical regime. These numerical results qualitatively agreed with previous experimental works regarding the initiation and propagation processes.

• Journal of Korean Association for Spatial Structures
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• v.20 no.4
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• pp.149-158
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• 2020

The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.41-49
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• 2008

We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition $$u_{tt}-u_{xx}=au+b{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha-1}{\upsilon}_+^{\beta}+s{\phi}_{00}+f,\\{\upsilon}_{tt}-{\upsilon}_{xx}=cu+d{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha}{\upsilon}_+^{{\beta}-1}+t{\phi}_{00}+g,$$ where ${\alpha},{\beta}>1$ are real constants, $u_+={\max}\{u,0\},\;s,\;t{\in}R,\;{\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator and f, g are ${\pi}$-periodic, even in x and t and bounded functions.

• 한국초전도학회:학술대회논문집
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• v.10
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• pp.99-102
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• 2000

We have studied the effects of d-wave symmetry on the critical current of YBa$_2$Cu$_3$O$_7$ step-edge Josephson junctions. The critical current along various misorientation angle was measured and analyzed with the concept of grain-boundary junctions with d-wave symmetry. Experimental results of c-oriented YBCO step-edge junctions with various in-plane misorientation angles were qualitatively in good agreement with the theory. The out-of-plane misorientation angle is usually formed between two grains with the c axes perpendicular to each other and is normally not controllable.

• Journal of the Korean Society for Railway
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• v.7 no.3
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• pp.200-207
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• 2004

Theoretical study has been conducted to clarify pressure characteristics of KTX (Korea Train eXpress) in tunnel. The severe pressure change in tunnel may give rise to the ear-discomfort for passenger and fatigue for car body. Critical tunnel lengths which are induced by x-t diagram analysis can be applied to the experimental results measured by using the running test with atmospheric pressure sensors and portable data acquisition system in previous study. In this study, the tunnels from 200m to 4000m in length have been chosen for the investigation of tunnel length effects. We found that there are similar patterns of external pressure change for each critical tunnel length. The critical tunnel lengths are governed by train speed, train length and sonic velocity. And, the patterns of pressure wave in tunnel are classified into eight groups.

• The Journal of the Acoustical Society of Korea
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• v.25 no.2E
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• pp.60-68
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• 2006

High-frequency bistatic scattering measurements from a corrugated surface were made in an acoustic water tank. First the azimuthal scattering pattern was measured from an artificially corrugated surface which has varying impedance. The corrugated surface was installed both transverse to the direction of incident wave and longitudinal to the direction of incident wave. The angle between the corrugated surface and the direction of the incident wave was about $45^{\circ}$. Second, the scattering strengths were measured from the flat sediment and the corrugated sediment. A critical angle of about $37^{\circ}$ was calculated in the acoustic water tank. The measurements were made at three fixed grazing angles: $33^{\circ}$ (lower than critical angle), $37^{\circ}$ (critical angle), and $41^{\circ}$ (higher than critical angle). The scattering angle and the grazing angle are equal in each measurement. Frequencies were from 50 kHz to 100 kHz with an increment of 1 kHz. The corrugated sediment was made transverse to the direction of the incident wave. The first measurement indicates that the scattering patterns depend on the relations between the corrugated surface and the direction of the incident wave. In the second measurement, the data measured from the flat sediment were compared to the APL-UW model and to the NRL model. The NRL model's output shows more favorable comparisons than the APL-UW model. In case of the corrugated sediment, the model and the measured data are different because the models used an isotropic wave spectrum of sediment roughness in the scattering calculations. The isotropic wave spectrum consists of $w_2$ and ${\gamma}_2$. These constants derived from sediment names or bulk size. The model which used the constants didn't consider the effect of a corrugated surface. In order to consider a corrugated surface, the constants were varied in the APL-UW model.

• Composites Research
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• v.20 no.1
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• pp.15-22
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• 2007

As a fundamental approach to studying elastic wave behaviors in fiber-reinforced composites, this paper introduces the analytical method to predict the modes, directions, and amplitudes of all reflected waves that are generated by free-surface reflection in fiber-reinforced composites. The paper also explores a new phenomenon where a reflected wave that is predicted to exist in accordance with the slowness surface may disappear. This may occur when the angle of incidence of a quasi-shear wave exceeds a newly defined critical angle, named the third critical angle. It is hoped that the analytical approach introduced in this paper will provide an easy-to-follow guideline for researchers in the relevant area such as ultrasonic nondestructive testing.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.661-677
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• 2002

The subject of this investigation is to study the buckling of cross-ply laminated orthotropic cylindrical thin shells with variable elasticity moduli and densities in the thickness direction, under external pressure, which is a power function of time. The dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a system of time dependent differential equations with variable coefficients by using Galerkin's method. Finally, the critical dynamic and static loads, the corresponding wave numbers, the dynamic factors, critical time and critical impulse are found analytically by applying a modified form of the Ritz type variational method. The dynamic behavior of cross-ply laminated cylindrical shells is investigated with: a) lamina that present variations in the elasticity moduli and densities, b) different numbers and ordering of layers, and c) external pressures which vary with different powers of time. It is concluded that all these factors contribute to appreciable effects on the critical parameters of the problem in question.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.329-343
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• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.