• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1317-1322
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• 2001

What changes in the eigen values and eigen functions are produced if the boundary surface S is no longer rigid but has a specific acoustic admittance which may vary from point to point on S. In this paper, changes in eigen values and eigen functions are derived by using Kirchhoff-Helmholtz integral equation. And acoustic potential energy, which is representative measure describing the physical quantity in cavity, is defined. Acoustic potential energy can be divided into primary one and secondary one. Primary one is the acoustic potential energy through unchanged eigen functions, and secondary one is through changed eigen functions. Using these two term, we can find the eigenvalue problem, which gives the control performance when the boundary condition is changed.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.173-185
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• 2014

In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.339-345
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• 1993

It is well known that distribution of functions of eigen values and vectors of a certain matrix plays an important role in multivariate analysis. This paper deals with the transformation of a correlation-type random matrix to its eigen values and vectors. Properties of the transformation are also considered. The results obtained are applied to express the joint distribution of eigen values and vectors of the correlation matrix when sample is taken from a m-variate spherical distribution.

• Journal of KSNVE
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• v.10 no.5
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• 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.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Structural Engineering and Mechanics
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• v.88 no.2
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• pp.109-115
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• 2023

In this paper, frequencies of zigzag structure of carbon nanotubes isinvestigated based on Donnell shell theory. These tubes are wrapped with the ring supports in the axial direction. The fundamental frequency curves displayed in article show the dependence of vibrations attributes to zigzag single walled carbon nanotubes. Various zigzag indices are introduced against the variation of length to predict the vibration. Also, the influence of ring supports is sketched with proposed structure for frequency analysis. The frequencies of zigzag tube decreases as the length increases. It is observed that the frequencies decreases with ring support and have higher frequencies without ring. The problem is formulated using Partial Differential Equation. Three expressions of modal deformation displacement functions is used for the elimination of temporal variation to form the solution in the eigen from. For the stability of present study the results are compared with experimentally and numerically in the open text.

• JSTS:Journal of Semiconductor Technology and Science
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• v.10 no.3
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• pp.203-212
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• 2010

In this paper, we present an analytical model for the first eigen energy level ($E_0$) of the carriers in the inversion layer in present generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. Commonly used approaches to evaluate $E_0$ make either or both of the following two assumptions: one is that the barrier height at the oxide-semiconductor interface is infinite (with the consequence that the wave function at this interface is forced to zero), while the other is the triangular potential well approximation within the semiconductor (resulting in a constant electric field throughout the semiconductor, equal to the surface electric field). Obviously, both these assumptions are wrong, however, in order to correctly account for these two effects, one needs to solve Schrodinger and Poisson equations simultaneously, with the approach turning numerical and computationally intensive. In this work, we have derived a closed-form analytical expression for $E_0$, with due considerations for both the assumptions mentioned above. In order to account for the finite barrier height at the oxide-semiconductor interface, we have used the asymptotic approximations of the Airy function integrals to find the wave functions at the oxide and the semiconductor. Then, by applying the boundary condition at the oxide-semiconductor interface, we developed the model for $E_0$. With regard to the second assumption, we proposed the inclusion of a fitting parameter in the wellknown effective electric field model. The results matched very well with those obtained from Li's model. Another unique contribution of this work is to explicitly account for the finite oxide-semiconductor barrier height, which none of the reported works considered.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.5
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• pp.233-241
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• 2000

This paper presents a systematic design procedure of $H_{\infty}$ controller of TCSC for damping low frequency inter-area oscillations in large power systems. Sensitivities of the inter-area mode for changes in line susceptance are computed using the eigen-sensitivity theory of augmented system matrix and TCSC locations are selected using the line sensitivities. The reduced model required for designing a manageable-size $H_{\infty}$ controller is obtained using the reduced frequency domain system identification method and the various weighting functions are tuned systematically to provide a robust performance. The proposed $H_{\infty}$ controller proved to be very effective for damping the inter-area mode of the large KEPCO power system.

• Journal of the Korean Society of Safety
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• v.7 no.2
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• pp.30-41
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• 1992

Analysis of Dynamic Characterisocs of Rectangular Plate by Finite Element Method. Dynamic characteristics of a rectangular plate with opening in it is studied by finite element method. To investigate these characteristics 12 degrees of freedom membrane finite element in used. The rectangular membrane finite elements are defined by specifying geometry, internal displacement functions and strain-displacement relations. Then, the governing equation for the finite element is derived by energy method. To derive the mass matrix and stiffness matrix of the element, expressions for strain and kineic energy in terms of the node displacement are generated. In constructing the overall structure matrix, the matrix of each elements are superposed and partitioned by applying the given boundary condition to obtain a nonslngular matrix. To find the natural freguencies and viration modes, the eigen values and the corresponding eigen vectors are computed by the computer using well known Jacobi power method. In order to verify the capability of the membrane finite element, a flat rectangular plate is analyzed first, and the result is compared with well known analytical results to show the good agreement. A rectangular plate with opening in It is analyzed with the same finite element. The results are presented in this paper. Unfortunately, the literature study could not provide with some results to compare, but the results reveal that the output of this research is phlslcally reasonable. And the results of this research are useful not only in practice but also for the future experimental research in comparison purpose.