• Current Optics and Photonics
• /
• 제5권5호
• /
• pp.491-499
• /
• 2021

A scalar Fourier modal method for the numerical analysis of the scalar wave equation in inhomogeneous space with an arbitrary permittivity profile, is proposed as a novel theoretical embodiment of Fourier optics. The modeling of devices and systems using conventional Fourier optics is based on the thin-element approximation, but this approach becomes less accurate with high numerical aperture or thick optical elements. The proposed scalar Fourier modal method describes the wave optical characteristics of optical structures in terms of the generalized transmittance function, which can readily overcome a current limitation of Fourier optics.

• Current Optics and Photonics
• /
• 제5권6호
• /
• pp.597-605
• /
• 2021

An extended Fourier modal method (FMM) for optical dipole radiation in three-dimensional photonic structures is proposed. The core elements of the proposed FMM are the stable bidirectional scattering-matrix algorithm for modeling internal optical emission, and a novel optical-dipole-source model that prevents numerical errors induced by the Gibbs phenomenon. Through the proposed scheme, the FMM is extended to model a wide range of source-embedded photonic structures.

• 소음진동
• /
• 제6권6호
• /
• pp.771-779
• /
• 1996

In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

• Journal of the Optical Society of Korea
• /
• 제16권3호
• /
• pp.196-202
• /
• 2012

We observe that the transmission and reflection efficiencies of a one-dimensional metallic grating under transverse-magnetic illumination calculated using the Fourier modal method (FMM) with the Fourier factorization rules have peculiar fluctuations, albeit small in magnitude, as the number of field harmonics increases. It is shown that when the number of Fourier terms for the electromagnetic field is increased from that in the conventional FMM, the fluctuations due to non-convergent highly evanescent eigenmodes can be eliminated. Our examination reveals that the fluctuations originate from the Gibbs phenomenon inherent in the Fourier-series representation of a permittivity function with discontinuities, and from non-convergence of highly evanescent internal Bloch eigenmodes.

• 소음진동
• /
• 제10권5호
• /
• pp.800-805
• /
• 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.

• Structural Engineering and Mechanics
• /
• 제16권6호
• /
• pp.655-674
• /
• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.

• 소음진동
• /
• 제10권3호
• /
• pp.536-550
• /
• 2000

본 연구에서는 유체가 채워진 환형공간을 갖는 편심 원통형 쉘의 모드 특성을 조사하였다. Stokes 변환을 응용한 Fourier 급수전개법으로 고유진동수를 구하는 방법을 전개하여 유체가 채워진 환형공간을 갖는 편심원통형 쉘에 대한 이론적인 해를 구하였고 이를 유한요소법에 의한 값과 비교하였다. 또한 편심된 정도가 원통형 쉘의 모드 특성에 미치는 영향을 검토하였고 편심율에 따른 이들의 특성도 고찰하였다.

• Structural Engineering and Mechanics
• /
• 제14권1호
• /
• pp.1-20
• /
• 2002

Investigated in this study are the modal characteristics of the eccentric cylindrical shells with fluid-filled annulus. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of eccentricity on the modal characteristics of the shells is investigated using a finite element modeling.

• Structural Engineering and Mechanics
• /
• 제14권4호
• /
• pp.417-434
• /
• 2002

This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

• 한국음향학회지
• /
• 제18권7호
• /
• pp.39-44
• /
• 1999

직사각형 평판의 고유진동수와 진동모드를 연구하였다. 이중 퓨리에 사인시리즈를 직사각형 평판의 모달 변위함수로 사용하였으며, 다양한 경계조건을 가지는 자유진동 해석에 적용하였다. 유한급수 전개로써 근사해를 나타내는 고전적인 Ritz 방법을 이용해서 직사각형 평판의 고유진동수를 해석한 Leissa의 결과와 본 연구의 결과를 비교하였다. 그리고, 평판의 형상비에 따른 영향도 연구하였다. 자유경계 평판, 외팔평판, 고정평판, 그리고 모서리가 단순지지된 직사각형 평판의 진동형태를 가시화 하였다.