• Title/Summary/Keyword: euler equation

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A Study on the efficient control of an elastic manipulator moving in a vertical plane (수직면에서 작동하는 탄성 매니퓰레이터의 효율적인 제어에 관한 연구)

  • 강준원;이중섭;권혁조;오재윤;정재욱
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.11a
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    • pp.318-322
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    • 1996
  • This paper presents a technique to control a robot which has a flexible manipulator moving in a vertical plane. The flexible manipulator is modeled as an Euler-Bernoulli beam. Elastic deformation is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID control technique. The proportional, integral and derivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and having a short settling time. The effectiveness of the developed control scheme is showed experimentally. In the position control experiment, three different end masses are used. The experimental results shows little overshoot, no steady state error, and less than 2.5 second settling time in case of having an end mass which is equivalent to 45% of the total system weight. Also the residual vibration of the end point is effectively controlled.

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Nonlinear Dynamic Analysis of a Large Deformable Beam Using Absolute Nodal Coordinates

  • Jong-Hwi;Il-Ho;Tae-Won
    • International Journal of Precision Engineering and Manufacturing
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    • v.5 no.4
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    • pp.50-60
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    • 2004
  • A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

An Experimental Study on the Characteristics of the Impulsive Wave Discharged from the Open End of a Bend Pipe (곡관출구로부터 방출되는 펄스파의 특성에 관한 실험적 연구)

  • 이동훈;김희동;뢰척구준명
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.9
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    • pp.406-413
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    • 2001
  • The current study depicts and experimental work of the impulsive wave discharged from the exit of several kinds of right-angle bend pipes, which are attached to the open end of a simple shock tube. The weak normal shock wave with Mach number from 1.02 to 1.20 is employed to obtain the impulsive wave propagating outside the exit of the pipe bends. The experimental data of the magnitude of the impulsive wave and its propagation directivity are analyzed to characterize the impulsive waves discharged from the right-angle bend pipes and compared with those from a straight pipe. The impulsive waves are visualized by a Schlieren optical system. A computation work using the two-dimensional, unsteady, compressible Euler equation is also carried out to represent the experimented impulsive waves. The results obtained show that a right-angle miter bend considerably reduces the magnitude of the impulsive wave and its directivity toward to the pipe axis, compared with the straight pipe. It is believed that the right angle miter bend pipe can play a role of passive control agianst the impulsive wave.

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Design and Control of Robot Arm for Inspection and Rescue Operations (재난 탐사 및 구조를 위한 로봇팔 설계 및 제어)

  • Kang, Jin-Il;Choi, Hyeung-Sik;Jun, Bong-Huan;Ji, Dae-Hyeong;Oh, Ji-Yoon;Kim, Joon-Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.11
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    • pp.888-894
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    • 2016
  • This paper presents the kinematic and dynamic analysis of the robot arm for inspection and rescue operations. The inspection robot arm has Pitch-Pitch-Pitch-Yaw motion for an optimal and stable view of the camera installed at the end of the manipulator. The rescue operation robot arm has Yaw-Pitch-Pitch-Roll motion to handle heavy tools. Additionally, both robot arms are waterproof, as they use the triple-layer O-ring. Furthermore, the dynamic equation including the damping force due to the mechanical seal for waterproofness was derived by using the Newton-Euler method. A control system using the ARM processor was developed and introduced in this paper, and its performance was verified through experiments.

Study on High Accurate Schemes for Simulation of Free-surface Flow (자유표면 유동 시뮬레이션을 위한 고정확도 수치도식의 검토)

  • Park, Jong-Chun;Lee, Byoung-Hyuk;Kim, Jeung-Hu
    • Journal of Ocean Engineering and Technology
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    • v.20 no.4 s.71
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    • pp.31-36
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    • 2006
  • Numerical schemes for spacing and time are tested to accurately simulate the wave propagation. The tested numerical schemesinclude 2nd-order central differencing, l-order upwind scheme, 2nd-order Leith scheme, 3rd-order MUSCLE, QUICK and QUICKEST schemes in spacing and the Euler and 4th-order Runge-Kutta(R-K) schemes in time. It is seen that more accurate results are expected when the higher-order schemes, especially the schemes combined with a TVD control limiter, are used for solving the wave equation. The 3rd-order upwind scheme with limiter and the 4th-order R-K scheme in tim£ are finally applied to the wave-making simulation in a digital wave tank.

Hull Form Design of Catamaran Type Dredging Vessel Using Model Test and Numerical Simulation (모형실험 및 수치 시뮬레이션을 이용한 쌍동형 준설선의 선형 설계에 관한 연구)

  • Lee Young-Gill;Son Choong-Yul;Jeong Uh-Cheul;Kang Dae-Sun;Jeong Kwang-Leol;Kim Do-Jung
    • Journal of Ocean Engineering and Technology
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    • v.20 no.2 s.69
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    • pp.66-71
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    • 2006
  • To develope a hull form of catamaran type dredging vessel, resistance characteristics is investigated to find the interaction effect of waves between the two hulls. Re fore body shape is simplified as two dimensional wedge shape for the maintenance and disassembly/assembly. Based on MAC method, numerical simulation is performed in staggered variable mesh system. Re conservation form of Euler equations and continuity equation are applied as governing equations. To verify numerical methods, the wive patterns along the hull surface are compared with the results of model tests. This study is performed as varying wedge shape of the bow and the distance between the two hulls. The wave interaction between two hulls are observed to investigate the relation the resistance performance and the flow characteristics. Suitable hull form and distance between two hulls are discussed.

Free vibration and harmonic response of cracked frames using a single variable shear deformation theory

  • Bozyigit, Baran;Yesilce, Yusuf;Wahab, Magd Abdel
    • Structural Engineering and Mechanics
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    • v.74 no.1
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    • pp.33-54
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    • 2020
  • The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

An Experimental Study on Nozzle Damping Characteristics for Combustion Instability Suppression (노즐감쇠 실험을 통한 연소 불안정 억제 연구)

  • Ryoo, Seunghyun;Kim, Junseong;Kim, Hakchul;Moon, Heejang;Lee, Dohyung
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2017.05a
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    • pp.724-729
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    • 2017
  • The interaction between the flow of the nozzle and the acoustic motion in the combustion chamber acts as an important factor in suppressing combustion instability where nozzle damping effect can be evaluated by nozzle admittance. In this study, Modified Impedance Tube experiment is implemented to predict the acoustic nozzle damping effect. The experimental admittances are compared to numerical admittances values which are calculated from one-dimensional linearized Euler equation of Crocco's theory. As a result, it was possible to identify qualitatively the tendency between increasing and decreasing parts. Also, Efficient frequency bands of nozzle attenuation can be predicted.

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Slender piezoelectric beams with resistive-inductive electrodes - modeling and axial wave propagation

  • Schoeftner, Juergen;Buchberger, Gerda;Benjeddou, Ayech
    • Smart Structures and Systems
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    • v.18 no.2
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    • pp.335-354
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    • 2016
  • This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

Dynamic Analysis of Constrained Mechanical System Moving on a Flexible Beam Structure(II) : Application (유연한 보 구조물 위를 이동하는 구속 기계계의 동력학 해석(II) : 응용)

  • Park, Chan-Jong;Park, Tae-Won
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.11
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    • pp.176-184
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    • 2000
  • Recently, it becomes a very important issue to consider the mechanical systems such as high-speed vehicle and railway train moving on a flexible beam structure. Using general approach proposed in the first part of this paper, it tis possible to predict planar motion of constrained mechanical system and elastic structure with various kinds of foundation supporting condition. Combined differential-algebraic equations of motion derived from both multibody dynamics theory and Finite Element Method can be analyzed numerically using generalized coordinate partitioning algorithm. To verify the validity of this approach, results from simply supported elastic beam subjected to a moving load are compared with exact solution from a reference. Finally, parameter study is conducted for a moving vehicle model on a simply supported 3-span bridge.

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