• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.310-323
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• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• Journal of The Korean Astronomical Society
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• v.28 no.1
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• pp.97-107
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• 1995

The stability of the geometrically thin, two-temperature hot accretion disk is studied. The general criterion for thermal instability is derived from the linear local analyses, allowing for advective cooling and dynamics in the vertical direction. Specifically, classic unsaturated Comptonization disk is analysed in detail. We find five eigen-modes: (1) Heating mode grows in thermal time scale, $(5/3)({\alpha}{\omega})^{-1}$, where alpha is the viscosity parameter and w the Keplerian frequency. (2) Cooling mode decays in time scale, $(2/5)(T_e/T_i)({\alpha}{\omega})^{-1}$, where $T_e\;and\;T_i$ are the electron and ion temperatures, respectively. (3) Lightman-Eardley viscous mode decays in time scale, $(4/3)(\Lambda/H)^2({\alpha}{\omega})^{-1}$, where $\Lambda$ is the wavelength of the perturbation and H the unperturbed disk height. (4) Two vertically oscillating modes oscillate in Keplerian time scale, $(3/8)^{1/2}\omega^{-1}$ with growth rate $\propto\;(H/\Lambda)^2$. The inclusion of dynamics in the vertical direction does not affect the thermal instability, adding only the oscillatory modes which gradually grow for short wavelength modes. Also, the advective cooling is not strong enough to suppress the growth of heating modes, at least for geometrically thin disk. Non-linear development of the perturbation is followed for simple unsaturated Compton disk: depending on the initial proton temperature perturbation, the disk can evolve to decoupled state with hot protons and cool electrons, or to one-temperature state with very cool protons and electrons.

• Wind and Structures
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• v.37 no.3
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• pp.191-209
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• 2023

This work investigates the subcritical free-shear prism wake at Re=22,000 by the Koopman analysis using the Dynamic Mode Decomposition (DMD) algorithm. The Koopman model linearized nonlinearities in the stochastic, homogeneous anisotropic turbulent wake, generating temporally orthogonal eigen tuples that carry meaningful, coherent structures. Phenomenological analysis of dominant modes revealed their physical interpretations: Mode 1 renders the mean-field dynamics, Modes 2 describes the roll-up of the Strouhal vortex, Mode 3 describes the Bloor-Gerrard vortex resulting from the Kelvin-Helmholtz instability inside shear layers, its superposition onto the Strouhal vortex, and the concurrent flow entrainment, Modes 6 and 10 describe the low-frequency shedding of turbulent separation bubbles (TSBs) and turbulence production, respectively, which contribute to the beating phenomenon in the lift time history and the flapping motion of shear layers, Modes 4, 5, 7, 8, and 9 are the relatively trivial harmonic excitations. This work demonstrates the Koopman analysis' ability to provide insights into free-shear flows. Its success in subcritical turbulence also serves as an excellent reference for applications in other nonlinear, stochastic systems.

• Proceedings of the KSR Conference
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• 2004.06a
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• pp.658-663
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• 2004

The interaction between a vibrating structure and a surrounding acoustic medium determines the acoustic power propagating into the far-field. A straightforward method to reduce the radiated power is to reduce the vibration of the structure. However it is more efficient to control the modes of the structure separately since each vibration mode of the structure has different radiation efficiency. An efficient method to reduce the sound radiation in the low frequency region is proposed by reducing the radiation efficiency of the structure.

• Journal of KSNVE
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• v.9 no.1
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• pp.189-195
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• 1999

The noise radiated by the rotary compressor for a room air-conditioner was investigated experimentally. Noise characteristics and structural eigen modes of the compressor were identified through sound tests and modal tests each other. From these tests. we found that the accumulator has a big contribution to the noise radiation. So, various structural modifications for the accumulator were performed and these modification methods were found efficient to the noise reduction from verification tests.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.159-167
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• 1996

This paper describes the theory and verification of a method which utilizes the free decay response of a structure to determine its vibration parameters. The theory of the method is base on the formulation of a system matrix, contains information characterizing the complete set of modal parameters of the system, and its eigen-solution problem. The applicability of the method is verified by simulated free decay response data of a cantilever bean The method described was used to determined the parameters related to the first five generated modes of vibration of a cantilever beam. It involves two very close natural frequencies which could not be identified using a frequency sweep test(peak amplitude) because of interference between modes.

• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.6
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• pp.594-607
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• 2013

A new efficient analytical eye-diagram determination technique for coupled interconnect lines is presented. Two coupled lines are decoupled into isolated eigen modes; bit blocks for coupled lines, which are defined as a block of consecutive bits, are then represented with decoupled modes. The crosstalk effects within the bit blocks are taken into account. Thereby, the crucial input bit patterns for the worst case eye-diagram determination are modeled mathematically, including inter-symbol interference (ISI). The proposed technique shows excellent agreement with the SPICE-based simulation. Furthermore, it is very computation-time-efficient in the order of magnitude, compared with the SPICE simulation, which requires numerous pseudo-random bit sequence (PRBS) input signals.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.11
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• pp.1613-1622
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• 2010

In this paper, the ultraprecision positioning control of an ultrasonic linear motor in a high-vacuum environment is presented. The bolt-clamped Langivin type transducer (BLT) with the 3rd longitudinal; and 6th lateral vibration modes was developed, which was excited by using the Eigen resonance frequency for two vibration modes in order to generate stable and high power. In practical applications, however, even if a geometrical design has an Eigen frequency, discordance between both mode frequencies can be generated by the contact mechanism and because of manufacturing errors as well as environmental factors. Both mode frequencies were precisely matched by adjusting the impedence. By using this method, the BLT can be driven under any environmental conditions. The nominal characteristic trajectory following(NCTF) control method was adopted to control the positioning of the system in vacuum. The developed linear motor stage show high positioning accuracy with 5 nm.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.539-551
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• 2005

Finite elements based on isoparametric formulation are known to suffer spurious stiffness properties and corresponding stress oscillations, even when care is taken to ensure that completeness and continuity requirements are enforced. This occurs frequently when the physics of the problem requires multiple strain components to be defined. This kind of error, commonly known as locking, can be circumvented by using reduced integration techniques to evaluate the element stiffness matrices instead of the full integration that is mathematically prescribed. However, the reduced integration technique itself can have a further drawback - rank deficiency, which physically implies that spurious energy modes (e.g., hourglass modes) are introduced because of reduced integration. Such instability in an existing stiffness matrix is generally detected by means of an eigenvalue test. In this paper we show that a knowledge of the dimension of the solution space spanned by the column vectors of the strain-displacement matrix can be used to identify the instabilities arising in an element due to reduced/selective integration techniques a priori, without having to complete the element stiffness matrix formulation and then test for zero eigenvalues.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.4
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• pp.168-176
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• 2000

This paper presents the Hessenberg method, a new sparsity-based small signal stability analysis program for large interconnected power systems. The Hessenberg method as well as the Arnoldi method computes the partial eigen-solution of large systems. However, the Hessenberg method with pivoting is numerically very stable comparable to the Householder method and thus re-orthogonalization of the krylov vectors is not required. The fractional transformation with a complex shift is used to compute the modes around the shift point. If only the dominant electromechanical oscillation modes are of concern, the modes can be computed fast with the shift point determined by Fourier transforming the time simulation results for transient stability analysis, if available. The program has been successfully tested on the New England 10-machine 39-bus system and Korea Electric Power Co. (KEPCO) system in the year of 2000, which is comprised of 791-bus, 1575-branch, and 215-machines. The method is so efficient that CPU time for computing five eigenvalues of the KEPCO system is 3.4 sec by a PC with 400 MHz Pentium IIprocessor.