• Title/Summary/Keyword: Galerkin`s Method

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The Study on New Radiating Structure with Multi-Layered Two-Dimensional Metallic Disk Array for Shaping flat-Topped Element Pattern (구형 빔 패턴 형성을 위한 다층 이차원 원형 도체 배열을 갖는 새로운 방사 구조에 대한 연구)

  • 엄순영;스코벨레프;전순익;최재익;박한규
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.13 no.7
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    • pp.667-678
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    • 2002
  • In this paper, a new radiating structure with a multi-layered two-dimensional metallic disk array was proposed for shaping the flat-topped element pattern. It is an infinite periodic planar array structure with metallic disks finitely stacked above the radiating circular waveguide apertures. The theoretical analysis was in detail performed using rigid full-wave analysis, and was based on modal representations for the fields in the partial regions of the array structure and for the currents on the metallic disks. The final system of linear algebraic equations was derived using the orthogonal property of vector wave functions, mode-matching method, boundary conditions and Galerkin's method, and also their unknown modal coefficients needed for calculation of the array characteristics were determined by Gauss elimination method. The application of the algorithm was demonstrated in an array design for shaping the flat-topped element patterns of $\pm$20$^{\circ}$ beam width in Ka-band. The optimal design parameters normalized by a wavelength for general applications are presented, which are obtained through optimization process on the basis of simulation and design experience. A Ka-band experimental breadboard with symmetric nineteen elements was fabricated to compare simulation results with experimental results. The metallic disks array structure stacked above the radiating circular waveguide apertures was realized using ion-beam deposition method on thin polymer films. It was shown that the calculated and measured element patterns of the breadboard were in very close agreement within the beam scanning range. The result analysis for side lobe and grating lobe was done, and also a blindness phenomenon was discussed, which may cause by multi-layered metallic disk structure at the broadside. Input VSWR of the breadboard was less than 1.14, and its gains measured at 29.0 GHz. 29.5 GHz and 30 GHz were 10.2 dB, 10.0 dB and 10.7 dB, respectively. The experimental and simulation results showed that the proposed multi-layered metallic disk array structure could shape the efficient flat-topped element pattern.

Dynamic Responses and Fuzzy Control of a Simply Supported Beam Subjected to a Moving Mass

  • Kong, Yong-Sik;Ryu, Bong-Jo;Shin, Kwang-Bok;Lee, Gyu-Seop;Lee, Hong-Gi
    • Journal of Mechanical Science and Technology
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    • v.20 no.9
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    • pp.1371-1381
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    • 2006
  • This paper deals with the active vibration control of a simply-supported beam traversed by a moving mass using fuzzy control. Governing equations for dynamic responses of a beam under a moving mass are derived by Galerkin's mode summation method, and the effect of forces (gravity force, Coliolis force, inertia force caused by the slope of the beam, transverse inertia force of the beam) due to the moving mass on the dynamic response of a beam is discussed. For the active control of dynamic deflection and vibration of a beam under the moving mass, the controller based on fuzzy logic is used and the experiments are conducted by VCM (voice coil motor) actuator to suppress the vibration of a beam. Through the numerical and experimental studies, the following conclusions were obtained. With increasing mass ratio y at a fixed velocity of the moving mass under the critical velocity, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam. With increasing velocity of the moving mass at a fixed mass ratio ${\gamma}$, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam too. The numerical predictions of dynamic deflection of the beam have a good agreement with the experimental results. With the fuzzy control, more than 50% reductions of dynamic deflection and residual vibration of the tested beam under the moving mass are obtained.

Dynamic response of functionally gradient austenitic-ferritic steel composite panels under thermo-mechanical loadings

  • Isavand, S.;Bodaghi, M.;Shakeri, M.;Mohandesi, J. Aghazadeh
    • Steel and Composite Structures
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    • v.18 no.1
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    • pp.1-28
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    • 2015
  • In this paper, the dynamic response of functionally gradient steel (FGS) composite cylindrical panels in steady-state thermal environments subjected to impulsive loads is investigated for the first time. FGSs composed of graded ferritic and austenitic regions together with bainite and martensite intermediate layers are analyzed. Thermo-mechanical material properties of FGS composites are predicted according to the microhardness profile of FGS composites and approximated with appropriate functions. Based on the three-dimensional theory of thermo-elasticity, the governing equations of motionare derived in spatial and time domains. These equations are solved using the hybrid Fourier series expansion-Galerkin finite element method-Newmark approach for simply supported boundary conditions. The present solution is then applied to the thermo-elastic dynamic analysis of cylindrical panels with three different arrangements of material compositions of FGSs including ${\alpha}{\beta}{\gamma}M{\gamma}$, ${\alpha}{\beta}{\gamma}{\beta}{\alpha}$ and ${\gamma}{\beta}{\alpha}{\beta}{\gamma}$ composites. Benchmark results on the displacement and stress time-histories of FGS cylindrical panels in thermal environments under various pulse loads are presented and discussed in detail. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem, and provide pertinent results that are instrumental in the design of FGS structures under time-dependent mechanical loadings.

Cost-effectiveness dynamics and vibration of soft magnetoelastic plate near rectangular current-carrying conductors

  • AliAsghar Moslemi Beirami;Vadim V. Ponkratov;Amir Ebrahim Akbari Baghal;Barno Abdullaeva;Mohammadali Nasrabadi
    • Structural Engineering and Mechanics
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    • v.88 no.2
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    • pp.159-168
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    • 2023
  • Cost-effective high precision hybrid elements are presented in a hierarchical form for dynamic analysis of plates. The costs associated with controlling the vibrations of ferromagnetic plates can be minimized by adequate determination of the amount of electric current and magnetic field. In the present study, the effect of magnetic field and electric current on nonlinear vibrations of ferromagnetic plates is investigated. The general form of Lorentz forces and Maxwell's equations have been considered for the first time to present new relationships for electromagnetic interaction forces with ferromagnetic plates. In order to derive the governing nonlinear differential equations, the theory of third-order shear deformations of three-dimensional plates has been applied along with the von Kármán large deformation strain-displacement relations. Afterward, the nonlinear equations are discretized using the Galerkin method, and the effect of various parameters is investigated. According to the results, electric current and magnetic field have different effects on the equivalent stiffness of ferromagnetic plates. As the electric current increases and the magnetic field decreases, the equivalent stiffness of the plate decreases. This is a phenomenon reported here for the first time. Furthermore, the magnetic field has a more significant effect on the steady-state deflection of the plate compared to the electric current. Increasing the magnetic field and electric current by 10-times results in a reduction of about 350% and an increase of 3.8% in the maximum steady-state deflection, respectively. Furthermore, the nonlinear frequency decreases as time passes, and these changes become more intense as the magnetic field increases.

Analysis of Electromagnetic Scattering by a Perfectly Conducting Strip Grating on Dielectric Multilayers (다층 유전체 위의 조기적인 도체 스트립 구조에 의한 전자파산란 해석)

  • 윤의중;양승인
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.8 no.2
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    • pp.161-172
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    • 1997
  • In this paper, electromagnetic scattering by a perfectly conducting strip grating on dielectric multilayers is analyzed for the normalized reflected and transmitted power by applying the Fourier-Galeakin moment method. The induced current density is expanded in a series of multiplication of chebyshev polynomials of the first kind and functions with appropriate edge boundary condition, the continuous condition of electromagnetic field is applied in the boundary planes. The confirm the validity of the proposed method, the nor- malized reflected and transmitted power obtained by varying the relative permittivity and thickness of each dielectric layers are evaluated and compared with those of the existing numerical method and a paper, and then the numerical results in this paper are in good agreement with those of the existing numerical method and the paper. The sharp variation position in the geometrically normalized reflected and transmitted power can be moved by the incident angle, grating period, and the relative permittivity and thickness of the dielectric multilayers, these sharp variation points which are called the Wood's anomaly of the Geome- trically normalized reflected power are observed as a main factor when the reflected powers of the higher order mode are transitted between propagating and evanescent modes, and the local minimum positions are slightly moved to the left hand direction in which grating period is getting small according to the increase of the relative permittivity of dielectric layers.

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