• 제목/요약/키워드: Point Mass Differential Equation

검색결과 9건 처리시간 0.025초

Analysis of slope stability based on evaluation of force balance

  • Razdolsky, A.G.;Yankelevsky, D.Z.;Karinski, Y.S.
    • Structural Engineering and Mechanics
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    • 제20권3호
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    • pp.313-334
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    • 2005
  • The paper presents a new approach for the analysis of slope stability that is based on the numerical solution of a differential equation, which describes the thrust force distribution within the potential sliding mass. It is based on the evaluation of the thrust force value at the endpoint of the slip line. A coupled approximation of the slip and thrust lines is applied. The model is based on subdivision of the sliding mass into slices that are normal to the slip line and the equilibrium differential equation is obtained as the slice width approaches zero. Opposed to common iterative limit equilibrium procedures the present method is straightforward and gives an estimate of slope stability at the value of the safety factor prescribed in advance by standard requirements. Considering the location of the thrust line within the soil mass above the trial slip line eliminates the possible development of a tensile thrust force in the stable and critical states of the slope. The location of the upper boundary point of the thrust line is determined by the equilibrium of the upper triangular slice. The method can be applied to any smooth shape of a slip line, i.e., to a slip line without break points. An approximation of the slip and thrust lines by quadratic parabolas is used in the numerical examples for a series of slopes.

Application of differential transformation method for free vibration analysis of wind turbine

  • Bozdogan, Kanat Burak;Maleki, Farshid Khosravi
    • Wind and Structures
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    • 제32권1호
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    • pp.11-17
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    • 2021
  • In recent years, there has been a tendency towards renewable energy sources considering the damages caused by non-renewable energy resources to nature and humans. One of the renewable energy sources is wind and energy is obtained with the help of wind turbines. To determine the behavior of wind turbines under earthquake loads, dynamic characteristics are required. In this study, the differential transformation method is proposed to determine the free vibration analysis of wind turbines with a variable cross-section. The wind turbine is modeled as an equivalent variable continuous flexural beam and blade weight is considered as a point mass at the top of the structures. The differential equation representing the free vibration of the wind turbine is transformed into an algebraic equation with the help of differential transformation method and the angular frequencies and the mode shapes of the wind turbine are obtained by the help of the differential transformation method. In the study, a sample taken from the literature was solved with the presented method and the suitability of the method was investigated. The same wind turbine example also modeled by finite element modelling software, ABAQUS. Results of the finite element model and differential transformation method are compared with each other and the results are in good agreement.

Vibration and stability of fluid conveying pipes with stochastic parameters

  • Ganesan, R.;Ramu, S. Anantha
    • Structural Engineering and Mechanics
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    • 제3권4호
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    • pp.313-324
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    • 1995
  • Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

자기부상 시스템을 이용한 임의의 금속구 부상을 위한 디지털제어기 설계 (Design of Digital Controller for the Levitation of Variable Steel Balls by using Magnetic Levitation System)

  • 사영호;이건영
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2001년도 하계학술대회 논문집 D
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    • pp.1940-1942
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    • 2001
  • Magnetic Levitation System(MLS) levitates a steel ball to the desired position in the gravity field using electromagnetic force. MLS consists of light sensor to measure the position of steel ball and an electromagnet to control the position of the ball, that composes a feedback control system. This work does not use a steel ball with constant mass but variable mass steel balls as magnetic levitation targets. Differential equation of electric circuit for electromagnet and motion equation of the movement of steel ball are derived for modeling nonlinear system, that will be linearized at the nominal operating point. We propose a digital control that can levitate a steel ball of which weight is not known for ED-4810 system. Algorithm for estimating ball weight and feedback control are implemented in digital scheme under pentium PC equiped with A/D and D/A converter, ACL-8112, using C-language. Simulation and experimental results are given to show the usefulness of the proposed controller.

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Exact vibration of Timoshenko beam combined with multiple mass spring sub-systems

  • El-Sayed, Tamer A.;Farghaly, Said H.
    • Structural Engineering and Mechanics
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    • 제57권6호
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    • pp.989-1014
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    • 2016
  • This paper deals with the analysis of the natural frequencies, mode shapes of an axially loaded beam system carrying ends consisting of non-concentrated tip masses and three spring-two mass sub-systems. The influence of system design and sub-system parameters on the combined system characteristics is the major part of this investigation. The effect of material properties, rotary inertia and shear deformation of the beam system is included. The end masses are elastically supported against rotation and translation at an offset point from the point of attachment. Sub-systems are attached to center of gravity eccentric points out of the beam span. The boundary conditions of the ordinary differential equation governing the lateral deflections and slope due to bending of the beam system including developed shear force frequency dependent terms, due to the sub.system suspension, have been formulated. Exact formulae for the modal frequencies and the modal shapes have been derived. Based on these formulae, detailed parametric studies are carried out. The geometrical and mechanical parameters of the system under study have been presented in non-dimensional analysis. The applied mathematical model is presented to cover wide range of mechanical, naval and structural engineering applications.

일반적인 단부조건을 갖는 보의 자유진동 (Free Vibrations of Generally Restrained Beams)

  • 신성철;김봉규;안대순;김선기
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2003년도 춘계학술대회논문집
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    • pp.864-869
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    • 2003
  • The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and point masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a range of non-dimensional system parameters.

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대공화기 탄자비행시간 계산 기법 (A Computation Method for Time of Flight in the Anti-Aircraft Gun Fire Control System)

  • 김재훈;김의환;유석진;김성호
    • 정보처리학회논문지:컴퓨터 및 통신 시스템
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    • 제4권11호
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    • pp.361-368
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    • 2015
  • 대공화기사격통제장치에서 유효사거리는 정지한 표적에 대해 충분한 파괴력을 가질 수 있도록 탄속이 음속 이상을 유지하는 거리로 정의되고 있다. 접근하는 표적은 탄과 표적 간 상대속도가 증가하므로 실질적인 교전 사거리는 위의 유효사거리보다 더욱 연장된다. 그러나 기존에 제시된 TOF 계산식은 유효사거리 내에서만 정확하고 유효사거리를 벗어나면 정확하지 못하다. 본 논문은 교전사거리를 보장할 수 있도록 유효사거리 내에서와 유효사거리 밖에서도 충분한 정확도를 가진 실시간 처리가 가능한 탄자비행시간 계산 기법을 제시한다. 시뮬레이션을 통해 30미리 대공 탄에 대한 본 논문의 유용성을 보인다.

토석류 유동층에서 토사체적 농도 특성에 관한 연구 (The Study of Sediment Volume Concentration in Liquefied-Layer of Debris Flow)

  • 김성덕
    • 한국지반환경공학회 논문집
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    • 제15권12호
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    • pp.109-115
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    • 2014
  • 본 연구의 목적은 산지에서 세립사가 포함된 유동체 혼합물이 다양한 경사 각도를 갖는 수로에서 공급유량의 변화에 따른 토사체적농도를 분석한 것이다. 수치모델은 질량보존 및 운동량 보존에 관한 방정식 그리고 세립토와 조립토 방정식에 기초하여 유한차분법을 이용하여 수행되었다. 비탈 경사면 각도 변화에 따른 토사농도 비교에서 경사가 급할수록 토사체적 농도의 급격한 변곡점이 나타났다. 공급유량의 변화에서는 공급유량이 많을수록 Fluctuation이 발생하였고, 토석류의 상태가 난류형으로 변하여 토사가 부유사 형태로 변화되었다. 이는 토석류의 이동속도가 빠르게 됨을 알 수 있다. 포화된 조립토의 변화에 따른 비교에서는 그 길이가 길수록 고농도가 발생하였으므로 사면 안정을 위해서는 사면에서의 침식 가능 여부를 먼저 판단해야 된다. 본 연구의 결과는 강우 변화에 따른 비탈면 하류단에서의 유동체 혼합물의 토석류에 의한 재해를 예측 및 다양한 경사의 비탈면을 갖는 산지 밑에서의 토석류에 의한 재해에 대한 정보를 제공할 것이다. 또한 사면 안정 시 효율적인 사면 경사각도로 설치하는 것과 사면에서의 침식 방지등에 있어 토석류와의 관계성 분석 및 토석류 재해를 막기 위한 다양한 대책을 세우는 데 효과적인 정보를 제공할 것이다.

수정된 증발법을 이용하여 제작된 주석 나노입자의 녹는점 강하에 관한 연구 (Study on the Melting Point Depression of Tin Nanoparticles Manufactured by Modified Evaporation Method)

  • 김현진;백일권;김규한;장석필
    • 대한기계학회논문집B
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    • 제38권8호
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    • pp.695-700
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    • 2014
  • 본 논문에서는 수정된 증발법을 이용하여 제작된 주석(Sn) 나노입자의 녹는점 강하 특성에 대한 연구를 진행하였다. 이를 위해 대량생산이 가능한 수정된 증발법을 이용하여 10nm 급 주석 나노입자를 제조하였다. 주석 나노입자 표면의 산화 방지를 위하여 Benzyl Alcohol 을 기본유체로 사용하였으며, 제작된 주석 나노입자의 형상과 입자크기를 알아보기 위하여 투과전자현미경(TEM)을 사용하였다. 제작된 나노입자의 녹는점은 시차주사열량계(DSC)를 통해 측정하였으며, 광전자분광분석기(XPS)를 사용하여 제작된 주석 나노입자의 성분 분석을 진행 하였다. 주석 나노입자의 녹는점은 주석의 녹는점인 $232^{\circ}C$보다 44% 감소한 $129^{\circ}C$로 측정되었다. 녹는점 측정 결과는 Gibbs-Thomson 식 및 Lai 의 식과 비교하였으며, 그 결과 Lai의 식이 실험결과를 잘 예측함을 확인할 수 있었다.