• Honam Mathematical Journal
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• v.30 no.3
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• pp.521-533
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• 2008

We investigate a periodically forced Lotka-Volterra type predator-prey system with impulsive perturbations - seasonal effects on the prey, periodic releasing of natural enemies(predator) and spraying pesticide at the same fixed times. We show that the solutions of the system are bounded using the comparison theorems and find conditions for the stability of a stable prey-free solution and for the permanence of the system.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.601-614
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• 2018

We consider the magnetic $Schr{\ddot{o}}dinger$ operator coupled with two different potentials. One of them is a harmonic oscillator and the other is a periodic potential. We give some periodic potential classes for which the operator has purely absolutely continuous spectrum. We also prove that for strong magnetic field or large coupling constant, there are open gaps in the spectrum and we give a lower bound on their number.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.12
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• pp.36-43
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• 2001

We evaluate the optical characteristics of planar distributed feedback (DFB) waveguides with quarter-wavelength phase-shifter. To analyze explicitly its band-pass and resonance properties, we present and newly develop a modal transmission-line theory (MTLT) based on Floquet's theorem and Babinet's principle. The numerical results reveal that this approach offers a simple and analytic algorithm to analyze either the filtering or the oscillating characteristic of DFB gratings with quarter-wavelength phase-shifter, and has a novel physical insight that may not be achieved in other approximating approaches

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.1991-1999
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• 2000

This research has been performed to reveal the hysteresis phenomena of the hunting motion in a railway passenger car having a bolster. Since linear analysis can not explain them, bifurcation analysis is used to predict its outbreak velocities in this paper. However bifurcation analysis is attended with huge computing time, thus this research proposes more effective numerical algorithm to reduce it than previous researches. Stability of periodic solution is obtained by adapting of Floquet theory while stability of equilibrium solutions is obtained by eigen-value analysis. As a result, linear and nonlinear critical speed are acquired. Full scale roller rig test is carried out for the validation of the numerical result. Finally, it is certified that there are many similarities between numerical and test results.

• Journal of KSNVE
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• v.7 no.5
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• pp.819-826
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• 1997

The finite element analyses of a composite hingeless rotor blade in forward flight have been performed to investigate the influence of blade design parameters on the blade stability. The blade structure is represented by a single cell composite box-beam and its nonclassical effects such as transverse shear and torsion-related warping are considered. The nonlinear periodic differential equations of motion are obtained by moderate deflection beam theory and finite element method based on Hamilton principle. Aerodynamic forces are calculated using the quasi-steady strip theiry with compressibility and reverse flow effects. The coupling effects between the rotor blade and the fuselage are included in a free flight propulsive trim analysis. Damping values are calculated by using the Floquet transition matrix theory from the linearized equations perturbed at equilibrium position of the blade. The aeroelastic results were compared with an alternative analytic approch, and they showed good correlation with each other. Some parametric investigations for the helicopter design variables, such as pretwist and precone angles are carried out to know the aeroelastic behavior of the rotor.

• Journal of KSNVE
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• v.8 no.6
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• pp.1086-1092
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• 1998

This paper presents a general analytical method for analyzing the instability of unbalanced electromagnetic forces produced in induction motors with an eccentric rotor. The equations to be solved are a set of second order differential equations which give matrices with periodic coefficients that are a function of time due to the unbalanced electromagnetic force. The method is based on an extension of the Floquet theory. A transfer matrix over one period of the motion is obtained. and the stability of the system can be determined with the eigenvalues of the matrix. The analysis results of instability zone were coincided upon comparing that of transfer matrix method with that of rotating frame. Two examples are given. including an industrial application. The results show that the method proposed is satisfactory.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.9
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• pp.53-63
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• 1994

In indoor radio systems, vehicular communication systems, and land mobile systems, a very important problem is that of maintaining stable communications at all locations. Therefore solutions for the indoor propagation problem are important aspects of the mobile communication system. leaky coxial cables are finding increasing use in communications systesm involving mines, tunnels, tailroads, and highways, and in new obstacle detection, or guided radar, schemes for ground transportation and perimenter surveilance. In this paper a leaky coaxial cable having periodic slots in the outer conductor is described to obtain the propagation modes in the various environments. We use aneccentric cylindrical model to develop the theory for surface-wave propagation on the cable. Numerical Results are also included for the propagation constants, field distribution and current distribution. First, we derive the electromagnetic equation for leaky coaxial cable having symmetrical periodic slots using mode-matching method and Floquet's theorem, and then find various modes, propagation constants, field distribution, etc.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.11
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• pp.1052-1057
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• 2010

Dynamic stability of rotating blade considering gravity effect is investigated in this paper. Equations of motion for the beam is derived by employing hybrid deformation variable method and transformed into dimensionless form. The present modeling method is verified by RecurDyn. Stability diagrams are presented to show the influence of the configuration of the beam and angular velocity on the dynamic stability by applying Floquet's theory. Since the natural frequencies are varied when the blade has rotating motion, it is found that relatively large unstable regions exist approximately 1.1 times as high as the first bending natural frequency and half of the sum of first and second bending natural frequency.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.2
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• pp.688-698
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• 2019

If heave motion in the platform causes horizontal parametric vibration of a Compliant Vertical Access Riser (CVAR), the riser may become unstable. A combination of riser parameters lies in the unstable region aggravates vibrational damage to the riser. Change of axial tensile stress in the riser combined with its natural frequency and mode shape change results in mode coupling. In accordance with the state transition matrices of the riser in the coupled and uncoupled states, the stable and unstable regions were obtained by Floquet theory, and the vibration response under different conditions was obtained. The parametric excitation of the CVAR is shown to occur mainly in first-order unstable regions. Mode coupling may cause parametric excitation in the least stable regions. Damping reduces the extent of unstable regions to a certain extent.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.189-196
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• 1996

Vibration of a beam translating over supports in vertical motion is investigated in this paper. Equations of motion are formulated using the virtual work principle by regarding the supports as kinematical constraints imposed on an unrestrained beam and by discretizing the beam via the assumed mode method. Differential-algebraic equations of motion are derived and reduced to differential equations in independent generalized coordinates by the generalized coordinate partitioning method. Geometric stiffness of the beam due to translating motion is considered and how the geometric stiffness of beam affects dynamic stability is also investigated. Instability of the beam. in various conditions is also investigated using Floquet theory and then the results are verified through the dynamic response analysis. Results of numerical simulation are presented for various prescribed motions of the beam.