• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.181-189
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

• Nuclear Engineering and Technology
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• v.17 no.4
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• pp.279-289
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• 1985

The purpose of this paper is to investigate the density-wave oscillation type instability in the recirculating loop of U-tube steam generator (UTSG). The perturbed and nodalized conservations equations based on the drift-flux model have been derived to obtain the single-and two-phase pressure drop perturbations, by taking into account the slip between phases, nonuniform heat flux and heated wall dynamics. To assess the stability, the frequency domain technique with the Nyquist criterion has been used under the constant pressure drop boundary condition through the loop. The computer implementation of this model, SASG, was used for the parametric study of the steam generator in Kori-Unit 1. The results of the parametric study revealed important factors influencing UTSG stability margin.

• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.3
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• pp.183-198
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• 2012

Dynamic buckling, also known as parametric resonance, is one of the dynamic instability phenomena which may lead to catastrophic failure of structures. It occurs when compressive dynamic loading is applied to the structures. Therefore it is essential to establish a reliable procedure to test and evaluate the dynamic buckling behaviors of structures, especially when the structure is designed to be utilized in compressive dynamic loading environment, such as supercavitating underwater vehicle. In the line of thought, a dynamic buckling test system is designed in this work. Using the test system, dynamic buckling tests including beam, plate, and stiffened plate are carried out, and the dynamic buckling characteristics of considered structures are investigated experimentally as well as theoretically and numerically.

• Journal of Astronomy and Space Sciences
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• v.20 no.3
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• pp.205-216
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• 2003

The attitude motion of a spin-stabilized, upper-stage spacecraft is investigated based on a two-body model, consisting of a symmetric body, representing the spacecraft, and a spherical pendulum, representing the liquid slag pool entrapped in the aft section of the rocket motor. Exact time-varying nonlinear equations are derived and used to eliminate the drawbacks of conventional linear models. To study the stability of the spacecraft's attitude motion, both the spacecraft and pendulum are assumed to be in states of steady spin about the symmetry axis of the spacecraft and the coupled time-varying nonlinear equation of the pendulum is simplified. A quasi-stationary solution to that equation and approximate resonance conditions are determined in terms of the system parameters. The analysis shows that the pendulum is subject to a combination of parametric and external-type excitation by the main body and that energy from the excited pendulum is fed into the main body to develop the coning instability. In this paper, numerical examples are presented to explain the mechanism of the coning angle growth and how angular momenta and disturbance moments are generated.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.5
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• pp.173-180
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• 1984

The spectra of scattering light fromlaser-produced plasma near its fundamental and second harmonic wavelength were observed respectively by means of spectroscopic technique. The experimental results and the generation mechanism of nonlinear effects such as the second garmonics and the brillouin scattering were analysed theoretically. The spectra of reflected laser light became wider than that of incident laser light. And the peak of spectrum of reflected light shifted to red-side from that of incident light. The second harmonic light is generated from the nonlinear interaction of the incident laser light and the electron plasma wave excited in resonance region by the oblique incidence of laser light to the plasma. The Brillouin backscattering from laser-produced plasmas of hydrogen and deuterium has shown an isotope effect in the red-side region of the generated second harmonic light. This isotope shift is explained by the parametric instability at the cutoff (resonance) region using frequency-and phase-matching conditions of the waves.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.718-723
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• 2000

Dynamic stability of an axially oscillating cantilever beam with a concentrated mass is investigated in this paper. The equations of motion are derived and the derived equations include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Under certain conditions of the frequency and the amplitude of oscillating motion, parametric instabilities may occur. The multiple scale perturbation method is employed to obtain the stability analysis results. It is found that the system stability varies with the magnitude or the location of the concentrated mass. Instability increases as the concentrated mass approaches to the free-end or its magnitude increases.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.159-168
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• 2005

Noise generated by the blunt trailing edge of lifting surfaces is investigated in this study using fluid structure interaction theory. First, through the eddy modeling, noise generation doe to the flow instability on the rigid trailing edge is surveyed. Then the behavior of elastic cantileverd beam is investigated. Parametric study based on various material properties is employed to analyze the motion of the beam. Moreover, each eigenmode approach of cantilevered beam is used to find when flow induced vibration is resonant. To analyze elastic behavior of cantilever beam efficiently, moving grid generation technique based on non-conservative form of Navier-Stokes equation is used. Equation of the motion associated with the cantilever beam is discretized by the Galerkin procedure with forced vibration. As a consequence, behavior of the elastic cantilevered beam is stable when the first mode natural frequency of the material is relatively higher than that of flow induced pressure fluctuation.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.233-241
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• 2003

The rolling schedule procedure has been an important part of the Enterprise Resource Planning (ERP) systems. The performance of production planning in an ERP system depends on the selection of the three parameters in rolling schedule procedure: frozen interval, replanning interval, and planning horizon (forecast window). This research investigated, in a theoretical approach, the combined impact of selections of those three parameters. The proven mathematical theorems provided guidance to re-duction of instability (nervousness) and to seek the optimal balance between stability and responsiveness of ERP systems. Further the theorems are extended to incorporate the cost structure.

• Journal of KSNVE
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• v.10 no.6
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• pp.991-997
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• 2000

The objective of this study is to examine the onset condition and the frequency characteristics of the low-frequency combustion oscillation in a surface burner. For this purpose, extensive parametric studies have been performed experimentally and the effects of size of each section, the equivalence ratio, and the entrance velocity on oscillatory behavior explored. The experimental results were discussed in comparison with the other combustors associated tilth the low-frequency combustion oscillation. The combustion mode is driven at high combustion rate by the lift of unstable flame near the lower limit of the combustible equivalence ratio. The oscillation frequency is dependent not on the burner geometry but on the equivalence ratio and the combustion load. Low-frequency combustion mode was formed to be divided into two different modes, named C1 and C2 respectively. Two modes occurred individually, simultaneously or transitionally according to the equivalence ratio and combustion load. The characteristics of low-frequency oscillation is different from each other depending on the type of combustors. The surface burner has also its own characteristics of low -frequency oscillation.