• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.152-163
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• 1999

The problem of eigenvalue and eigenvector for v-notched cracks in pseudo-isotropic and anisotropic dissimilar materials was obtained to discuss stress singularities from traction free boundary and perfect bonded interface conditions assuming like the form of complex stress function for v-notched cracks in an isotropic material. Eigenvalues were solved by a commercial numerical program, MATHEMATICA. The relation between wedged angle and material property for eigenvalue, ${\lambda}$ indicating stress singularities of v-notched cracks in pseudo-isotropic and anisotropic dissimilar materials was examined.

• KIEE International Transactions on Power Engineering
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• v.4A no.2
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• pp.79-83
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• 2004

A new small signal stability analysis method for eigenvalue analysis is presented. This method utilizes the Resistive Companion Form (RCF) for the computation of the transition matrix over a specified time interval, which corresponds to a single cycle operation of the system. This method is applicable to any system, with or without switching element. An illustrative example of the method is presented and the eigenvalues are compared with those of the conventional state space method (analog) in order to demonstrate the accuracy of the proposed eigenvalue analysis method. Also, the variations of oscillation modes that are caused by the switching operation can be precisely analyzed using this method.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.129-139
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• 2000

The problem of eigenvalue and eigenvector is obtained from a V-notched crack in pseudo-isotropic dissimilar materials by the traction free boundary and the perfect bonded interface conditions. The complex stress function is assumed as the two-term William's type. The eigenvalue is solved by a commercial numerical program, MATHEMATICA to discuss stress singularities for V-notched cracks in pseudo-isotropic dissimilar materials. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination to eigenvector coefficients associated with eigenvalues. The RWCIM algorithm is also coded by the MATHEMATICA.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.49-53
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• 2011

In this paper, we adopt a numerical method to establish the smallest set to contain all Ger$\v{s}$gorin discs of a given complex matrix and its some similar matrices. With the smallest set, a new estimation for all eigenvalues of the matrix is obtained.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.648-654
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• 2023

Schwarz lemma at the non-smooth boundary point for holomorphic self-map on the intersection of two balls in ℂ² is obtained. At the complex tangent point in the corner of the boundary of the domain, the tangential eigenvalue of the complex Jacobian of the holomorphic map is estimated if the map is transversal.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.546-552
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• 2012

This paper is a study on squeal noise simulation under the consideration of temperature and pressure dependent material properties of friction material. For this, data of pressure and temperature dependent material properties of lining is achieved by using lining data base and exponential curve fit. Complex eigenvalue analysis is performed for predicting squeal noise frequency and instability and chassis dynamo test is performed for achieving squeal noise frequency, sound pressure level, occurrence temperature & pressure. Initial multi models are composed for considering complex interface conditions such as pad ear-clip, piston-housing and guide pin-torque member. The simulation result of base models is compared with the test result. Squeal noise simulation under the consideration of temperature and pressure dependent material properties of friction material is performed and analyzed using multi models. And additional condition is disc material property variation. Entire simulation conditions are combined and analyzed. Finally, this paper proposes direction of the warm squeal noise model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.3
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• pp.325-331
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• 2013

In this study, a complex eigenvalue analysis is implemented to verify the unstable mode of a brake system using ABAQUS software. The component participation factors and component modal participation factors are used to analyze the total contributions from each component and each component mode to a particular unstable system mode. This study shows that the 1.4-kHz unstable system mode comes from mode coupling between the 2nd nodal diametric mode and 3rd lateral axial mode (LAM) in the baseline model. A sensitivity analysis with a linking index is performed to prevent the mode coupling of the component modes. This linking index analysis shows the optimum mass loading position to move away the natural frequency of the 3rd LAM, which contributes to the unstable mode. Finally, a complex eigenvalue analysis is implemented with mass loading in the tie bar position, and no unstable system mode is generated in the low-frequency range (below 2 kHz).

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.7
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• pp.47-53
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• 2004

In this paper we introduce a complex escalator (ESC) structure-Equalizer and investigate its performance in complex channels in QPSK undulation systems. The proposed complex equalizer has the complete orthogonalization property and is independent of eigenvalue spread ratio (ESR) of channel. The proposed complex ESC equalizer shows as 7 times faster convergence speed as that of the conventional complex TDL equalizer algorithms in a complex channel model for QPSK systems.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.271-286
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• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1271-1286
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• 2015

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.