• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1790-1800
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• 2006

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. Performance of various orthogonal polynomials is compared to each other in terms of their efficiency and accuracy in determining the required natural frequencies. Orthogonal polynomials and functions studied in the present work are: Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the special trigonometric functions used in conjunction with Hermite cubics, and beam characteristic orthogonal polynomials. A total of 5 cases of beam boundary conditions and rotation are studied for their natural frequencies. The obtained natural frequencies and mode shapes are compared to those available in various references and the results for coupled flexural-torsional vibrations are especially compared to both previously available references and with those obtained using NASTRAN finite element package. Among all the examined orthogonal functions, Legendre orthogonal polynomials are the most efficient in overall CPU time, mainly because of ease in performing the integration required for determining the stiffness and mass matrices.

• 전기의세계
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• 제22권3호
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• pp.49-62
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• 1973

An algorithm for the state estimation and identification of multivariable nonlinear systems with noisy nonlinear observation has been investigated on the basis of the multidimensional Hermitian expansion for the a posteriori probability densities of the predicted observation, the predicted state and the observation conditioned by the state. A new approach for construction of this sequential nonlinear estimator, retaining up to the second order term of the observation error, has been developed, along with the approximation of nonlinear system functions, truncating at the second term. The estimation of the unknown parameters has been established by extending the state estimation technique, regarding the parameters as another state variables. The results of investigation indicate the feasibility of the schemes presented in this paper.

• International Journal of CAD/CAM
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• 제9권1호
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• pp.55-60
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• 2010

Quadratic B$\acute{e}$zier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic B$\acute{e}$zier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing $G^1$ quadratic B$\acute{e}$zier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the $G^1$ quadratic B$\acute{e}$zier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2007년도 하계종합학술대회 논문집
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• pp.93-94
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• 2007

이 논문은 시간도약 다중접속(time hopping multiple access: THMA) 초광대역(ultra wideband: UWB) 시스템에서 Modified Hermite Polynomial(MHP)을 기저펄스로 사용하는 M진 고속전송 기법을 제안하고, 시스템의 성능을 분석한다. MHP 펄스 차수들의 상호간 직교성을 이용하여 서로 다른 차수의 MHP 기저펄스 N개를 선형결합하여 M진으로 전송한다. MHP 기저펄스의 상호상관 함수를 구하여 제안하는 M진 시스템의 이론적인 성능을 분석하고, 모의실험을 통해서 기존의 M진 전송에 비해서 시스템의 비트오류확률(bit error rate: BER)이 개선됨을 보인다.

• Structural Engineering and Mechanics
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• 제23권5호
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.34-37
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• 1987

Theoretical calculations are presented for analying lateral modes of stripe geometry lasers. The solution technique affords a matching between the fields of the active layer and those of the surrounding passive layer. The fields are written as a liner combination of Hermite-Gaussian function. Therefore fields have been described with a single H - G function. The lowest-order mode spreading is calculated and related to the gain distribution.

• Journal of Power Electronics
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• 제9권1호
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• pp.61-67
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• 2009

In this paper, a simple technique is presented for robust stability testing of perturbed DC-DC converters having multi-linear uncertainty structure. This technique provides a necessary and sufficient condition for testing robust stability. It is based on the corollary of Routh criterion and gridding of parameters. The previous work based on parametric control theory using Kharitonov's theorem and Hermite Biehler theorem gives conservative results and only the sufficient condition of stability, whereas the proposed method provides the necessary and sufficient condition for testing robust stability and it is computationally efficient. The superiority of the method is compared with the Edge theorem.

• 오토저널
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• 제12권2호
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• pp.29-42
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• 1990

Three dimensional frame structures with such nonlinearities as large displacements, medium rotations, plastic hinges and local defects are efficiently analyzed by introducing the nonlinear rotational spring. Formulations are based on the incremental updated Lagrangian descriptions and the virtual work principle, Axial displacement and twisted angle in beam elements are interpolated linearly, while bending displacements are approximated by the Hermite polynomials. The modified are length method is used as a solution method. The moment-angle of rotation relationship obtained analytically or experimentally can be easily incorporated into the solution procedure. Several examples tested show that the present method can be used efficiently in analyzing nonlinear frame structures with plastic hinges or local defect.

• Korean Journal of Hydrosciences
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• 제5권
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• pp.85-97
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• 1994

A hybrid finite difference method for the longitudinal dispersion equation, which is based on combining the Holly-Preissmann scheme with fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme, is described and comparatively evaluated with other characteristics-based numerical methods. Longitudinal dispersion of an instantaneously-loaded pollutant source is simulated, and computational results are compared with the exact solution. The present method is free from wiggles regardless of the Courant number, and exactly reproduces the location of the peak concentration. Overall accuracy of the computation increases for smaller value of the weighting factor, $\theta$of the model. Larger values of $\theta$ overestimates the peak concentration. Smaller Courant number yields better accuracy, in general, but the sensitivity is very low, especially when the value of $\theta$ is small. From comparisons with the hybrid method using cubic interpolating polynomial and with splitoperator methods, the present method shows the best performance in reproducing the exact solution as the advection becomes more dominant.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.