• 제목/요약/키워드: Lagrange Equation

검색결과 294건 처리시간 0.021초

Efficient crosswell EM Tomography using localized nonlinear approximation

  • Kim Hee Joon;Song Yoonho;Lee Ki Ha;Wilt Michael J.
    • 지구물리와물리탐사
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    • 제7권1호
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    • pp.51-55
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    • 2004
  • This paper presents a fast and stable imaging scheme using the localized nonlinear (LN) approximation of integral equation (IE) solutions for inverting electromagnetic data obtained in a crosswell survey. The medium is assumed to be cylindrically symmetric about a source borehole, and to maintain the symmetry a vertical magnetic dipole is used as a source. To find an optimum balance between data fitting and smoothness constraint, we introduce an automatic selection scheme for a Lagrange multiplier, which is sought at each iteration with a least misfit criterion. In this selection scheme, the IE algorithm is quite attractive for saving computing time because Green's functions, whose calculation is a most time-consuming part in IE methods, are repeatedly re-usable throughout the inversion process. The inversion scheme using the LN approximation has been tested to show its stability and efficiency, using both synthetic and field data. The inverted image derived from the field data, collected in a pilot experiment of water-flood monitoring in an oil field, is successfully compared with that derived by a 2.5-dimensional inversion scheme.

위상 변경 고유치 재해석 기법을 이용한 최적 구조물 동특성 변경 (Optimal Structural Dynamics Modification Using Eigen Reanalysis Technique of Technique of Topological Modifications)

  • 이준호;박영진;박윤식
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2003년도 춘계학술대회논문집
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    • pp.77-81
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    • 2003
  • SDM (Structural Dynamics Modification) is a tool to improve dynamic characteristics of a structure, more specifically of a base structure, by adding or deleting auxiliary (modifying) structures. In this paper, the goal of the optimal SDM is set to maximize the natural frequency of a base plate structure by attaching serially-connected beam stiffeners. The design variables are chosen as positions of the attaching beam stiffeners, where the number of stiffeners is considered as a design space. The problem of non-matching interface nodes between the base plate and beam stiffeners is solved by using localized Lagrange multipliers, which act to glue the two structures with non-matching interface nodes. As fer the cases of non-matching interface nodes problem, the governing equation of motion of a structure can be considered from the viewpoint of a topological modification, which involves the change of the number of structural members and DOFs. Consequently, the eigenpairs of the beam-stiffened plate structure are obtained by using an eigen reanalysis technique of topological modifications. Evolution Strategies (ES), which is a probabilistic population-based optimization technique that mimics the principles from biological evolution in nature, is utilized as a mean for the optimization.

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심해저 채광시스템의 단순 모델에 대한 분산 제어 기법 적용성 연구 (Study on the Application of Decentralized Control Method for Simplified Model of Deep Seabed Mining System)

  • 여태경;홍섭;김형우;최종수
    • 한국해양공학회:학술대회논문집
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    • 한국해양공학회 2004년도 학술대회지
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    • pp.73-78
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    • 2004
  • The deep seabed mining system is generally composed of surface vessel, lifting system, buffer, flexible pipe and miner. The milling system is regarded as a large-scale system in which each subsystem is interconnected to other one. In order to control a large-scale system, a decentralized control approaches have been proposed recently. In this paper, as a basic study on application of decentralized control, firstly, the mining system is simplified modeled, where the lifting system and buffer is regarded as a spherical pendulum and tile flexible pipe is as a two-dimension linear spring. Based on the derived model, the system characteristics and the feasibility of decentralized control are analyzed.

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Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre

  • Katariya, Pankaj V.;Panda, Subrata K.;Hirwani, Chetan K.;Mehar, Kulmani;Thakare, Omprakash
    • Smart Structures and Systems
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    • 제20권5호
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    • pp.595-605
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    • 2017
  • The present article reported the thermal buckling strength of the sandwich shell panel structure and subsequent improvement of the same by embedding shape memory alloy (SMA) fibre via a general higher-order mathematical model in conjunction with finite element method. The geometrical distortion of the panel structure due to the temperature is included using Green-Lagrange strain-displacement relations. In addition, the material nonlinearity of SMA fibre due to the elevated thermal environment also incorporated in the current analysis through the marching technique. The final form of the equilibrium equation is obtained by minimising the total potential energy functional and solved computationally with the help of an original MATLAB code. The convergence and the accuracy of the developed model are demonstrated by solving similar kind of published numerical examples including the necessary input parameter. After the necessary establishment of the newly developed numerical solution, the model is extended further to examine the effect of the different structural parameters (side-to-thickness ratios, curvature ratios, core-to-face thickness ratios, volume fractions of SMA fibre and end conditions) on the buckling strength of the SMA embedded sandwich composite shell panel including the different geometrical configurations.

Damped dynamic responses of a layered functionally graded thick beam under a pulse load

  • Asiri, Saeed A.;Akbas, Seref D.;Eltaher, Mohamed A.
    • Structural Engineering and Mechanics
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    • 제75권6호
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    • pp.713-722
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    • 2020
  • This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).

소형 디스크 드라이브에 있어서 베이스 강성이 회전하는 원판에 미치는 동적영향 분석 (Dynamic Analysis of the Effect of Base Flexibility on a Spinning Disk Dynamics in a Small Size Disk Drive)

  • 이성진;홍순교;정영민
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2001년도 춘계학술대회논문집B
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    • pp.601-606
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    • 2001
  • Free vibration analysis was performed for a spinning disk/spindle system mounted on a flexible baseplate. A simplified model was presented considering the effects of the baseplate flexibility on a disk/spindle system, and the equations of motion were derived by the assumed mode method and Lagrange's equation. From the results of the tree vibration analysis, the variations of the natural frequencies were investigated by changing rotating speed, baseplate thickness. They were attributed to the coupling between the flexible modes of the spinning disk/spindle system and the baseplate. This simplified model was used to predict the dynamic characteristics of a small size disk drive. The validity of the simplified model was verified by experiments and FE analysis.

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4절링크를 기반으로 하는 신개념 ATC 메커니즘의 동역학 해석 (Dynamic Modeling of a Novel ATC Mechanism based on 4-bar Linkage)

  • 이상호;김종원;서태원;김종원
    • 제어로봇시스템학회논문지
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    • 제22권4호
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    • pp.307-314
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    • 2016
  • Recently, demands on the tapping machine are increased due to the case of a cell phone is changed to metal such as aluminum. The automatic tool changer (ATC) is one of the most important devices for the tapping machine related to the speed and energy consumption of the machine. To reduce the consumed energy and vibration, the dynamic modeling is essential for the ATC. In this paper, inverse dynamic modeling of a novel ATC mechanism is introduced. The proposed ATC mechanism is composed of a double four-bar mechanism with a circular tablet to generate continuous rotation of the tablet. The dynamic modeling is performed based on the Lagrange equation with a modeling for the contact between the four-bar and the tablet. Simulation results for various working conditions are proposed and analyzed for the prototype design. The dynamic modeling can be applied to determine the proper actuator and to reduce the vibration and consumed energy for the ATC machine.

예산 제약과 예약 정책이 있는 복수 제품 신문 배달 소년 문제 해결을 위한 효율적 방법론 (An Efficient Method for Solving a Multi-Item Newsboy Problem with a Budget-Constraint and a Reservation Policy)

  • 이창용
    • 산업경영시스템학회지
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    • 제37권1호
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    • pp.50-59
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    • 2014
  • In this paper, we develop an efficient approach to solve a multiple-item budget-constraint newsboy problem with a reservation policy. A conventional approach for solving such problem utilizes an approximation for the evaluation of an inverse of a Gaussian cumulative density function when the argument of the function is small, and a heuristic method for finding an optimal Lagrangian multiplier. In contrast to the conventional approach, this paper proposes more accurate method of evaluating the function by using the normalization and an effective numerical integration method. We also propose an efficient way to find an optimal Lagrangian multiplier by proving that the equation for the budget-constraint is in fact a monotonically increasing function in the Lagrangian multiplier. Numerical examples are tested to show the performance of the proposed approach with emphases on the behaviors of the inverse of a Gaussian cumulative density function and the Lagrangian multiplier. By using sensitivity analysis of different budget constraints, we show that the reservation policy indeed provides greater expected profit than the classical model of not having the reservation policy.

Forced vibration of a functionally graded porous beam resting on viscoelastic foundation

  • Alnujaie, Ali;Akbas, Seref D.;Eltaher, Mohamed A.;Assie, Amr
    • Geomechanics and Engineering
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    • 제24권1호
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    • pp.91-103
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    • 2021
  • This paper concerns with forced dynamic response of thick functionally graded (FG) beam resting on viscoelastic foundation including porosity impacts. The dynamic point load is proposed to be triangle point loads in time domain. In current analysis the beam is assumed to be thick, therefore, the two-dimensional plane stress constitutive equation is proposed to govern the stress-strain relationship through the thickness. The porosity and void included in constituent is described by three different distribution models through the beam thickness. The governing equations are obtained by using Lagrange's equations and solved by finite element method. In frame of finite element analysis, twelve-node 2D plane element is exploited to discretize the space domain of beam. In the solution of the dynamic problem, Newmark average acceleration method is used. In the numerical results, effects of porosity coefficient, porosity distribution and foundation parameters on the dynamic responses of functionally graded viscoelastic beam are presented and discussed. The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.

수직면에서 회전운동 하는 단일 탄성링크를 가지는 매니퓰레이터의 모델링과 제어에 관한 연구 (A Study on the Modeling and Control of a Flexible One-Link Manipulator Moving in a Vertical Plane)

  • 김종대;오석형;김기호;오재윤
    • 한국정밀공학회지
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    • 제13권11호
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    • pp.132-142
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    • 1996
  • This paper presents a technique to model and control a manipulator which has a flexible link and moves in a vertical plane. The flexible link is modeled as an Euler-Bernoulli Beam. Elastic deformation of the flexible link 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. This paper presents a simple technique to improve the correctness of the developed model. The final model including the shortening effect due to elastic deformation correlates very well with experimental results. The free body motion simulation shows that two assumed modes for the representation of the elastic deformation is proper in terms of the model size and correctness. A control algorithm is developed using PID control technique. The proportional, integral and derivative control gains are determined based on dominant pole placement method with a rigid one-link manipulator. A position control simulation shows that the control algorithm can be used to control the position and residual oscillation of the flexible one-link manipulator effectively.

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