• Title/Summary/Keyword: Approximate Equation

Search Result 487, Processing Time 0.026 seconds

Error Evaluation of the Linearized Equation of Servo Valve in Hydraulic Control Systems (유압 서보 제어계에서 밸브 선형화 방정식의 오차 평가)

  • Kim, Tae-Hyung;Lee, Ill-Yeong
    • Proceedings of the KSME Conference
    • /
    • 2001.11a
    • /
    • pp.501-506
    • /
    • 2001
  • In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. In this study, the authors estimate computational errors in the process of applying the existing linearized equation stated above. For evaluating the computational accuracy in practical applications of the linearized equations, dynamic behaviors of hydraulic control systems are investigated through simulations with several kinds of representative hydraulic systems and the linearized equations suggested in this study.

  • PDF

Inverse Kinematics of a Serial Manipulator : Redundancy and a Closed-rom Solution by Exploting Geomertiric Constraints (원료불출기의 역기구학 : 여유자유도와 구속조건을 이용한 닫힌 형태의 해)

  • 홍금식;김영민;최진태;신기태;염영일
    • Proceedings of the Korean Society of Precision Engineering Conference
    • /
    • 1996.04a
    • /
    • pp.661-665
    • /
    • 1996
  • An inverse kinemetics problem of a reclaimer which digs and transports ironstones or coals in the raw yard is investigated. Because of the special features of the reclaimer of which scooping buckets are attached around the rotating drum at the end of boom, kinematic redundancy occurs in determining the joint varialbes For a given reclaiming point in space the forward kinematics yields 3 equations, however the number of involved variables in the equations are four. A plane equation approximating the surface near a reclaiming point is obtained by considering 8 adjacent points surrounding the reclaiming point. One extra equation to overcome redunduncyis further obtained from the condition that the normal vector at a reclaiming point is perpendicular to the plane. An approximate solution for a simplified problem is first discussed, Numerical solution for the oritinal nonlinear porblem with a constraint equation is also investigated. Finally a closed form solution which is not exact but sufficiently close enough is proposed by exploiting geometric constraint.

  • PDF

THE USE OF ITERATIVE METHODS FOR SOLVING NAVEIR-STOKES EQUATION

  • Behzadi, Shadan Sadigh;Fariborzi Araghi, Mohammad Ali
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.1_2
    • /
    • pp.381-394
    • /
    • 2011
  • In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

Error Analysis of Approximate Solution by Differential Transform Method with respect to Non-linearity of Duffing Equation (미분변환법을 이용해 구해진 Duffing Equation 근사해의 비선형성 증가에 따른 오차 분석)

  • Yang, Seong-Uk;Kim, Dong-Hun;Kim, Bong-Gyun;Yang, Jun-Mo;Lee, Sang-Cheol
    • 한국항공운항학회:학술대회논문집
    • /
    • 2015.11a
    • /
    • pp.20-24
    • /
    • 2015
  • 미분변환법은 미분방정식의 해를 구하기 위한 방법으로 다양한 분야에서 적용에 관한 연구를 수행 중이다. 항공우주분야의 동역학 모델링의 경우 미분방정식은 비선형성을 포함하게 되며 일반적으로 수치해석을 이용해 근사해를 구하게 된다. 본 논문에서는 미분변환법을 이용해 구해진 근사해의 오차 추이를 분석한 내용을 다루고 있다. 이를 위한 예제로써 duffing equation을 사용하였으며, duffing equation에 포함된 비선형성을 증가시킴에 따라 미분변환법을 이용해 구한 근사해와 수치해석을 이용해 구한 수치해를 비교하였다.

  • PDF

Analysis of Laminar Flow and Heat Transfer in Asymmetric, Sudden Expansion Channel (비대칭급확대채널의 층류유동 및 열전달 해석)

  • Won, Seung-Ho;Maeng, Joo-Sung;Son, Byung-Jin
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
    • /
    • v.13 no.1
    • /
    • pp.5-13
    • /
    • 1984
  • This analysis of numerical procedure is prediction of laminar flow and heat transfer at two dimension and steady flow in asymmetric sudden expansion channel. At former study, to analyse the flows with separation, the full Navier-Stokes equation is used, but there are many difficulties to analyse, and although significant progress has been made in the development of efficient computational methods for the Navier-Stokes equations, very large computation times are still required. In case of reward-facing flow, boundary-layer equation is used instead of full Navier-Stokes equation to analyse velocity fields, and result of this numerical analysis is good agreement with the given experimental study. In this case, since the computer time required for the boundary-layer calculation is an order of magnitude less than required for the solution of the full Navier-Stokes equation, this boundary-layer model provides a good approximate solution.

  • PDF

An Approximate Formulation for Scattering by Very Thin Dielectric Scatters (얇은 유전체의 산란특성 해석을 위한 근사식)

  • Koh, Il-Suek
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
    • /
    • v.15 no.8
    • /
    • pp.765-774
    • /
    • 2004
  • In this paper, a novel approximate solution for scattering by a very thin planar homogeneous dielectric scatterer with an arbitrary shape is formulated. This solution is based on a volumetric integral equation and is expressed in terms of Fourier transform. It is shown that the obtained solution is reduced to an exact solution for an infinite dielectric slab. For 2D, or 3D scatterers, the formulation is verified numerically. Especially fur edge-on TM polarized wave incidence a closed-form solution of backscattering from a thin dielectric half-plane is formulated, which is very accurate for wide range of normalized surface impedance except very low impedances(│η│〈0.5).

Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

  • Kim, Kook-Hyun;Kim, Byung-Hee;Choi, Tae-Muk;Cho, Dae-Seung
    • International Journal of Naval Architecture and Ocean Engineering
    • /
    • v.4 no.3
    • /
    • pp.267-280
    • /
    • 2012
  • An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

Effects of photostrictive actuator and active control of flexible membrane structure

  • Gajbhiye, S.C.;Upadhyay, S.H.;Harsha, S.P.
    • Smart Structures and Systems
    • /
    • v.14 no.2
    • /
    • pp.71-83
    • /
    • 2014
  • The purpose of this paper is to investigate the flexible structure of parabolic shell using photostrictive actuators. The analysis is made to know its dynamic behavior and light-induced control forces for coupled parabolic shell. The effects of an actuator location as well as membrane and bending components under the control action have been analyzed considering the approximate spherical model. The parabolic membrane shell accuracy is being mathematically approximated and validated comparing the light induced control forces using approximate equivalent spherical shell model. The parabolic shell with kapton smart material and photostrictive actuators has been used to formulate the governing equation in the transverse direction. The Kirchhoff-Love assumptions are used to obtain the governing equation of shell with actuator. The mechanical membrane forces and bending moments for parabolic thin shell with actuator is used to analyze the dynamic effect. The results show that membrane control action is much more significant than bending control action. Photostrictive actuators oriented along circumferential direction (actuator-2) can give better control effect than actuators placed along longitudinal direction (actuator-1). The slight difference is observed between spherical and parabolic shell for a surface with focal length to the diameter ratio of 1.00 or more than unity. Space applications often have the shape of parabolical shells or shell of revolution, due to their required focusing, aiming, or reflecting performance. The present approach is focused that photostrictive actuators can effectively control the vibration of parabolical membrane shell. Also, the actuator's location plays an important role in defining the control force.

A Study on the Prediction-Formulas of Approximate Estimate Based on Actual Work Cost for Subway (실적공사비에 의한 지하철 공사비 예측모형에 관한 연구)

  • Park, Jong-Hyuk;Jeon, Yong-Bae;Park, Hong-Tae
    • Journal of the Society of Disaster Information
    • /
    • v.9 no.1
    • /
    • pp.11-21
    • /
    • 2013
  • This study proposed cost prediction equation model by considering duration, construction, size, actual cost with the subway construction started by the actual cost system which was introduced since 2004. Costs - scale exponent n(confidence range: 0.5 to 0.7) for cost prediction of subway construction was drawn total cost(0.713), net cost(0.77) in point of the 11 subway construction data. The cost prediction equation model of the subway construction which was presented in this study is able to effectively apply to business planning, preliminary investigation, feasibility study, basic design stage to estimate the approximate cost in the future.

Construction Cost Estimate Modeling of Roundabout at Preliminary Design Stage in Jeju (제주도 내 회전교차로의 초기공사비 예측모델 개발)

  • An, Jin-Hong;Lee, Dong Wook
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.34 no.4
    • /
    • pp.1299-1306
    • /
    • 2014
  • Recently, there are many roundabouts installation works which are ordered to provide convenient transportation to road users as well as to eliminate traffic accidents and traffic delays. This study propose an approximate construction cost estimation model for early stages of roundabout construction. The model is designed considering the conditions of the early stage roundabout construction sites in Jeju. The regression equation of approximate construction cost was derived through regression analysis of 25 design data of roundabout construction in Jeju, and it was analyzed to have a high prediction accuracy. Finally, results verifies high prediction accuracy of the derived regression equation. Difference between the estimation cost and the design cost was only 2.3%, 3.7%, and 5.8% that verifies the high accuracy of the proposed approximate construction cost estimation model.