• 제목/요약/키워드: Kirchhoff equations

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비대칭 공기흡입구를 통해 전파하는 소음의 방사특성에 관한 수치적 연구 (Numerical Investigation on Radiation Characteristics of Noise Propagating through Asymmetry Aero-Intake)

  • 박용환;김민우;이규호;이수갑
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2007년도 추계학술대회논문집
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    • pp.1476-1481
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    • 2007
  • Numerical investigation on radiation characteristics of discrete frequency noise from asymmetry aero-intakes was carried out. The near-field predictions were obtained by solving the linearized Euler equations with computational aeroacoustic techniques consisting of high order finite difference scheme, non-reflecting boundary conditions, oversetgrid techniques. For the prediction of far-field directivity pattern, the Kirchhoff integral method was applied. By comparing the directivities of noise radiating from the scarf and the scoop aero-intakes with that from an axisymmetric aero-intake, it is shown that noise reduction at downward peak radiation angle can be achieved. The scattering of the radiating acoustic wave by background mean flow shifts the peak lobe radiation angle toward ground and increases the amplitude of the acoustic pressure compared with the cases without mean flow effect.

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Size-dependent damped vibration and buckling analyses of bidirectional functionally graded solid circular nano-plate with arbitrary thickness variation

  • Heydari, Abbas
    • Structural Engineering and Mechanics
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    • 제68권2호
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    • pp.171-182
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    • 2018
  • For the first time, nonlocal damped vibration and buckling analyses of arbitrary tapered bidirectional functionally graded solid circular nano-plate (BDFGSCNP) are presented by employing modified spectral Ritz method. The energy method based on Love-Kirchhoff plate theory assumptions is applied to derive neutral equilibrium equation. The Eringen's nonlocal continuum theory is taken into account to capture small-scale effects. The characteristic equations and corresponding first mode shapes are calculated by using a novel modified basis in spectral Ritz method. The modified basis is in terms of orthogonal shifted Chebyshev polynomials of the first kind to avoid employing adhesive functions in the spectral Ritz method. The fast convergence and compatibility with various conditions are advantages of the modified spectral Ritz method. A more accurate multivariable function is used to model two-directional variations of elasticity modulus and mass density. The effects of nanoscale, in-plane pre-load, distributed dashpot, arbitrary tapering, pinned and clamped boundary conditions on natural frequencies and buckling loads are investigated. Observing an excellent agreement between results of current work and outcomes of previously published works in literature, indicates the results' accuracy in current work.

동일 평면상에서 연성된 Mindlin 판 구조물의 에너지흐름유한요소해석 (Energy Flow Finite Element Analysis(EFFEA) of Coplanar Coupled Mindlin Plates)

  • 박영호
    • 대한조선학회논문집
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    • 제53권4호
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    • pp.307-314
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    • 2016
  • Energy flow analysis(EFA) is a representative method that can predict the statistical energetics of structures at high frequencies. Generally, as the frequency increases, the shear distortion and rotatory inertia effects in the out-of-plane motion of beams or plates become important. Therefore, to predict the out-of-plane energetics of coupled structures in the high frequency range, the energy flow analyses of Timoshenko beam and Mindlin plate are required. Unlike the energy flow model of Kirchhoff plate, the energy flow model of Mindlin plate is composed of three kinds of energy governing equations(out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave). This paper performed the energy flow finite element analysis(EFFEA) of coplanar coupled Mindlin plates. For EFFEA of coplanar coupled Mindlin plates, the energy flow finite element formulation of out-of-plane energetics in the Mindlin plate was performed. The general EFFEA program was implemented by MATLAB® language. For the verification of EFFEA of Mindlin plate, the various numerical applications were done successfully.

속도변동성분을 갖는 회전디스크의 횡진동 안정성 해석 (Stability Analysis of Transverse Vibration of a Spinning Disk with Speed Fluctuation)

  • 신응수;이기녕;신태명;김옥현
    • 한국소음진동공학회논문집
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    • 제12권1호
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    • pp.21-28
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    • 2002
  • This paper intends to investigate the effects of speed fluctuation caused by the cogging torque in permanent magnetic motors on the stability of the transverse vibration for a spinning disk. Based on the Kirchhoff\`s plate theory and the assumed mode methods, a set of discretized equations of motion were derived for an annular disk rotating with a harmonically varying speed. Then, a perturbation method using the multiple time scales was employed and stability boundaries were determined explicitly in terms of the magnitude and frequency of speed fluctuation, a nominal sped and the modal characteristics of the disk. It is found that parametric resonance occurs at several speed ranges and a single mode or a combination of two modes are involved to cause instability. It is also observed that unstable regions become broadened as the spinning speed increases or two modes are combined in parametric instability. As numerical simulations, stability analysis of a conventional CD-ROM drive was performed. Results of this work can e used as guidelines for motor design and operations with low vibration.

유한 요소법과 부분 구조 합성법을 이용한 회전 디스크-스핀들 계의 진동 해석 (Vibration Analysis of Rotating Disk-Spindle System Using Finite Element Method and Substructure Synthesis)

  • 정명수;장건희
    • 대한기계학회논문집A
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    • 제24권9호
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    • pp.2201-2210
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    • 2000
  • Vibration of a rotating disk-spindle system is analyzed by using Hamilton's principle, FEM and substructure synthesis. A rotating disk undergoes the rigid body motion and the elastic deformation. It s equation of motion is derived by Kirchhoff plate theory and von Karman nonlinear strain. A rotating shaft is described by Rayleigh beam theory considering the axial rigid body motion. The stationay shaft supporting the rotating disk-spindle-bearing system is modeled by Euler beam theory, and the stiffness of ball bearing is determined by A.B.Jones' theory. FEM is used to solve the derived governing equations, and substructure synthesis is introduced to assemble each structure of the rotating disk-spindle system. The developed theory is applied to the spindle system of a 35' computer hard disk drive with 3 disks to verify the simulation results. The simulation results agree very well with the experimental ones. The proposed theory may be effectively expanded to the complex structure of a disk-spindle system.

음향 홀로그래피를 이용한 방사 음장의 전방예측 방법에 관한 기본 이론 및 신호처리 방법 (The Forward Prediction of Radiation Sound Field Using Acoustic Holography : Basic Theory and Signal Processing Method)

  • 김양한;권휴상
    • 대한기계학회논문집
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    • 제16권9호
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    • pp.1654-1668
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    • 1992
  • 본 연구에서는 경험적으로 측정점 사이의 간격과 구경의 크기를 정하는 방법 에 대하여 살펴보았다.이에 반하여 둘러싸기 오차(wraparound error)는 이산화된 파수 성분 데이타의 처리 과정에서 발생하게 되는데, 이를 줄이기 위한 방법의 일환으 로 본 논문에서는 제로패딩(zero padding)방법을 도입하였다. 또한 둘러싸기 오차 (wraparound error)의 크기를 정량화하여 신뢰할 수 있는 예측결과의 범위를 살펴보았 다.

In-plane and out-of-plane waves in nanoplates immersed in bidirectional magnetic fields

  • Kiani, Keivan;Gharebaghi, Saeed Asil;Mehri, Bahman
    • Structural Engineering and Mechanics
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    • 제61권1호
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    • pp.65-76
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    • 2017
  • Prediction of the characteristics of both in-plane and out-of-plane elastic waves within conducting nanoplates in the presence of bidirectionally in-plane magnetic fields is of interest. Using Lorentz's formulas and nonlocal continuum theory of Eringen, the nonlocal elastic version of the equations of motion is obtained. The frequencies as well as the corresponding phase and group velocities pertinent to the in-plane and out-of-plane waves are analytically evaluated. The roles of the strength of in-plane magnetic field, wavenumber, wave direction, nanoplate's thickness, and small-scale parameter on characteristics of waves are discussed. The obtained results show that the in-plane frequencies commonly grow with the in-plane magnetic field. However, the transmissibility of the out-of-plane waves rigorously depends on the magnetic field strength, direction of the propagated transverse waves, small-scale parameter, and thickness of the nanoplate. The criterion for safe transferring of the out-of-plane waves through the conducting nanoplate immersed in a bidirectional magnetic field is also explained and discussed.

급성 동정맥루를 포함하는 인체 심혈관계의 혈류역학적 거동에 관한 수치 해석적 연구 (Computational Study on the Hemodynamic Behaviors of the Human Cardiovascular System with an Acute Arteriovenous Fistula)

  • 변수영;손정락;심은보;노승탁
    • 대한의용생체공학회:의공학회지
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    • 제24권4호
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    • pp.329-337
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    • 2003
  • 선천적 혹은 후천적인 이유로 인하여 인체 특정 부위의 정맥과 동맥이 서로 관통하여 동맥계의 혈류가 말초 혈관계를 우회하여 정맥계로 흐르게 되는 동정맥루는 인체 심혈관계의 혈류 역학적 거동에 큰 영향을 미치게 된다. 본 연구에서는 lumped parameter 모델을 기반으로 하는 수치 해석 방법을 사용하여 우측 하지에 위치한 급성 동정맥루가 전체 심혈관계에 미치는 영향을 해석적으로 고찰하였다. 이를 위하여 동정맥루가 포함된 인체 심혈관계를 전기 회로 상사계로 구성하였으며. 부위별 혈압과 관련된 상미분 연립 방정식을 4차의 Runge-Kutta방법으로 풀어서 시간에 따른 혈류 역학적 변수들을 구하였다 이때 급성 동정맥루의 생성에 따른 혈류 역학적 보상작용을 분석하기 위하여 arterial baroreflex 제어계를 모델에 포함하였다.

Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method

  • Singh, Piyush P.;Azam, Mohammad S.
    • Advances in nano research
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    • 제10권1호
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    • pp.25-42
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    • 2021
  • In this article, the vibration behavior of embedded Functionally Graded Nanoplate (FGNP) employing nonlocal Kirchhoff's plate theory has been investigated under hygrothermal environment. The FGNP is considered to be supported by Winkler-Pasternak foundation. The Eringen's differential theory is used for size effect on the vibration of the FGNP. Rayleigh-Ritz method with orthogonal polynomials are employed for the governing equations and edge constraints. The advantage of this method is that it overcomes all the drawbacks of edge constraints and can easily handle any combinations of mixed edge constraints. The coefficients viz. moisture expansion, thermal expansion and elastic coefficients are considered to be transversely graded across the FGNP. The similarity of the calculated natural frequencies is examined with the previous research, and a good concurrency is seen. The objective of this article is to analyze the parameters' effect on the nondimensionalized frequency of embedded FGNP under hygrothermal environment subjected to all possible edge constraints. For this, uniform and linear rise of temperature and moisture concentration are considered. The study highlights that the nonlocal effect is pronounced for higher modes. Moreover, the effect of the Pasternak modulus is seen to be prominent compared to the Winkler modulus on non dimensionalized frequencies of FGNP.

Management of the energy harvesting for MEMS/NEMS via newmark current method

  • Shang, Kun;Shan, Huafeng;Alkhalaf, Salem;Marzouki, Riadh;Khadimallah, Mohamed Amine
    • Advances in nano research
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    • 제12권6호
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    • pp.567-581
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    • 2022
  • The free and forced vibration in addition to electric energy harvesting of a piezoelectric disk resting on two-parameter foundation modeled by modified couple stress as well as Kirchhoff plate theory is probed. The governing equations and boundary conditions are obtained using Hamilton's principle. Then, the free and forced vibration are solved using numerical solutions, generalized differential quadrature method (GDQM) and Newmark-beta method. The forced vibration is resulted from a base excitation load. Also, the possible voltage which can be harvested from this system is obtained using generalized integral quadrature method. The validity of the formulation and solution procedure is confirmed using a compassion study. The impact of parameters such as length effect, inner to outer radius ratio, and foundations parameters on the free and forced vibration as well as energy harvesting is investigated in detail. This paper can be a basis for future studies in the area of piezoelectric harvesters in small scales.