• International Journal of Fluid Machinery and Systems
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• v.9 no.4
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• pp.338-353
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• 2016

Information on the surge behaviors and stall stagnation boundaries for a nine-stage axial flow compressor are summarized on the basis of analytical data in comparison with those for a single-stage one, with attention to the pressure ratio effect. The general trends of the surge loop behaviors of the pressure-mass flow are similar for both compressors including the fact that the subharmonic surges tend to appear very near the stall stagnation boundaries. With respect to the nine-stage compressor, however, the mild loops in the subharmonic surges tend to be very small in size relative to the deep loops, and at the same time, insufficient surge recovery phenomenon, which is a kind of subharmonic surge, appears also far from the stagnation boundary for relatively short delivery flow-paths. The latter is found to be a rear-stage surge caused by unstalling and re-stalling of the rear stages with the front-stages kept in stall in the stalled condition of the whole compressor, which situation is caused by stage-wise mismatching in the bottom pressure levels of the in-stall multi-stage compressor. The fundamental information on the stall stagnation boundaries is given by a group of normalized geometrical parameters including relative delivery flow-path length, relative suction flow-path length, and sectional area-pressure ratio, and by another group of normalized frequency parameters including relative surge frequencies, modified reduced resonance frequencies, and modified reduced surge frequencies. Respective groups of the normalized parameters show very similar tendency of behaviors for the nine-stage compressor and the single-stage compressor. The modified reduced resonance frequency could be the more reasonable parameter suggesting the flow-induced oscillation nature of the surge phenomena. It could give the stall stagnation boundary in a more unified manner than the Greitzer's B parameter.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.511-516
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• 2013

We establish an easy proof of an integral identity using the unitary invariance, which is applied to compare harmonicity and M-harmonicity.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.83-90
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• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• International Journal of Fluid Machinery and Systems
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• v.7 no.4
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• pp.160-173
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• 2014

Surge phenomena in multi-stage axial flow compressors were studied with attention to the frequency behaviors. A new parameter "volume-modified reduced surge frequency" was introduced, which took into consideration the essential surge process, i.e., emptying and filling of the working gas in the delivery plenum. The behaviors of the relative surge frequencies at the stall stagnation boundaries, compared with the corresponding duct resonance frequencies, have demonstrated the existence of two types of surges; i.e., a near-resonant surge and a subharmonic surge. The former, which has fundamentally a near-resonance frequency, occurs predominantly at the stall stagnation boundary for the short -and-fat plenum delivery flow-path and the long-and-narrow delivery duct flow-path, and possibly in the intermediate conditions. The latter, which has a subharmonic frequency of the fundamental near-resonant one and occurs mainly in the intermediate zone, is considered to be caused by the reduced frequency restricted to a limited range. In relation with those dimensionless frequencies at the stall stagnation boundary, the surge frequency behaviors in more general situations away from the boundaries could be estimated, though very roughly.

• Proceedings of the Optical Society of Korea Conference
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• 2000.02a
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• pp.276.2-278
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• 2000

In a recent years, a number of approaches have been studied, including passive, active, and hybrid mode-locking of semi-conductor lasers for short pulse generation and research has been devoted to achieve low timing-jitter operation since the timing jitter is unfavorable for system applications. Among the methods of mode locking, passive mode locking does not need external rf drives, and therefore the operation and fabrication procedures are simplified. In spite of these attractive advantages of passive mode-locked laser, it has critical drawbacks such as large timing jitter and the difficulty in synchronization with external circuits. Their inherent large timing jitter value was shown to be suppressed to certain levels by means of hybrid mode-locking technique$^{(1)}$ , where the saturable absorber section was modulated by an external signal with the cavity round trip frequency. Furthermore, the subharmonic mode-locking (SHML) technique alleviates the restrictions of high speed driving electronics. It has been demonstrated experimentally$^{(1)}$ that the hybrid subharmonic mode-locking technique has lead to significant reduction of the timing jitter. (omitted)

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.3
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• pp.462-469
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• 2001

In this paper, local oscillator in K band using low frequency noise upconversion gain anaylsis was designed and measured. We extended Two Signal Method(TSM) to estimate upconversion gain and resulting phase noise. To confirm the validity of the proposed method, a free-running oscillator which had low upconversion gain was designed. The measured oscillation frequency was 23.42 GHz and phase noise at 1 MHz of offset was -105.2 dBc/Hz. Also, this oscillator was operated for subharmonic injection locked osci1lator(SILO). In this case, SILO showed ideal frequency multiplier phase noise characteristics at low subharmonic injection power level.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.690-695
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• 2005

Flexible circular cantilever beams when excited externally introduce a lot of dynamic characteristics. The non-linear elements that these flexible beams develop include non-linearity due to inertia terms, spring, and damping. They show different characteristics of motion from each other. In the modes of lower order, the non-linearity due to spring is prevalent, while the non-linearity due to inertia Is prevalent in the modes of higher order. To analyze these effects the non-linear phenomena are analyzed experimentally. When the response characteristics of non-linear vibration are analyzed using autospectrum, it is possible to analyze the subharmonic and superharmonic mot ion by comparison. The phase change is analyzed using the method of phase portrait and the non-linear characteristics of response characteristics that are developed in flexible structures can be predicted and applied to the stage of design.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.767-782
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• 2022

In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.