• Title/Summary/Keyword: Nonlinear equations

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Finite Element Analysis of Fluid Flows with Moving Boundary

  • Cha, Kyung-Se;Park, Jong-Wook;Park, Chan-Guk
    • Journal of Mechanical Science and Technology
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    • v.16 no.5
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    • pp.683-695
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    • 2002
  • The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.

Numerical Study of Compression Waves Propagating Through Porous Walls (다공벽을 전파하는 압축파에 관한 수치해석적 연구)

  • Kim, Hui-Dong;Setoguchi, Toshiaki
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.11
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    • pp.1403-1412
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    • 1997
  • When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates through the tunnel, compressing and accelerating the rest air in front of the wave. At the exit of the tunnel, an impulsive wave is emitted outward toward the surrounding, which causes a positive impulsive noise like a kind of sonic boom produced by a supersonic aircraft. With the advent of high-speed train, such an impulsive noise can be large enough to cause the noise problem, unless some attempts are made to alleviate its pressure levels. In the purpose of the impulsive noise reduction, the present study calculated the effect of porous walls on the compression wave propagating into a model tunnel. Two-dimensional unsteady compressible equations were differenced by using a Piecewise Linear Method. Calculation results show that the cavity/porous wall system is very effective for a compression wave with a large nonlinear effect. The porosity of 30% is most effective for the reduction of the maximum pressure gradient of the compression wave front. The present calculation results are in a good agreement with experimental ones obtained previously.

A Study on High Performance Controller Design of Elastic Maniplator (탄성매니퓰레이터의 고성능 제어기 설계에 관한 연구)

  • Lee, Ji-U;Han, Seong-Hyeon;Lee, Man-Hyeong
    • Journal of the Korean Society for Precision Engineering
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    • v.9 no.3
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    • pp.73-82
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    • 1992
  • An industrial robot, installed real manufacturing processes an element of the system autmation, can be considered as an uncertain system due to dynamic uncertainties in inertial parameters and varying payloads. Most difficuties in controlling a robot manipulator are caused by the fact that the dynamic equations describing the motions of the manipulator are inherently nonlinear and heavily coupled effects between joints and associated links. Existing robot conrol systems have constant predefined gains and do not cover the complex dynamic interactions between manipulator joints. As a result, the manipulator is severly limited in range of application, speed of operation and variation of payload. The proposed controller is operated by adjusting its gains based on the response of the manipulator in such a way that the manipulator closely matches the reference model trajectories defined by the desinger. The proposed manipulator studied has two loops, an inner loop of model reference adaptive controller and an outer loop of state feedback controller with integral action to guarantee the stability of the adaptive scheme. This adaptation algorithm is based on the hyperstailiy approach with an improved Lyapunov function. The coupling among joints and the nonlinearity in the dynamic equation are explicitly considered. The designed manipulator controller shows good tracking performance in practical working environment, various load variations and parameter uncertainties.

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A nonlocal strain gradient theory for scale-dependent wave dispersion analysis of rotating nanobeams considering physical field effects

  • Ebrahimi, Farzad;Haghi, Parisa
    • Coupled systems mechanics
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    • v.7 no.4
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    • pp.373-393
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    • 2018
  • This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton's principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

Effect of higher order terms of Maclaurin expansion in nonlinear analysis of the Bernoulli beam by single finite element

  • Zahrai, Seyed Mehdi;Mortezagholi, Mohamad Hosein;Mirsalehi, Maryam
    • Structural Engineering and Mechanics
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    • v.58 no.6
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    • pp.949-966
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    • 2016
  • The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.

Higher order flutter analysis of doubly curved sandwich panels with variable thickness under aerothermoelastic loading

  • livani, Mostafa;MalekzadehFard, Keramat;Shokrollahi, Saeed
    • Structural Engineering and Mechanics
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    • v.60 no.1
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    • pp.1-19
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    • 2016
  • In this study, the supersonic panel flutter of doubly curved composite sandwich panels with variable thickness is considered under aerothermoelastic loading. Considering different radii of curvatures of the face sheets in this paper, the thickness of the core is a function of plane coordinates (x,y), which is unique. For the first time in the current model, the continuity conditions of the transverse shear stress, transverse normal stress and transverse normal stress gradient at the layer interfaces, as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the sandwich panel are satisfied. The formulation is based on an enhanced higher order sandwich panel theory and the vertical displacement component of the face sheets is assumed as a quadratic one, while a cubic pattern is used for the in-plane displacement components of the face sheets and the all displacement components of the core. The formulation is based on the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear approximation, the one-dimensional Fourier equation of the heat conduction along the thickness direction, and the first-order piston theory. The equations of motion and boundary conditions are derived using the Hamilton principle and the results are validated by the latest results published in the literature.

Modeling of unreinforced brick walls under in-plane shear & compression loading

  • Kalali, Arsalan;Kabir, Mohammad Zaman
    • Structural Engineering and Mechanics
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    • v.36 no.3
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    • pp.247-278
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    • 2010
  • The study of the seismic vulnerability of masonry buildings requires structural properties of walls such as stiffness, ultimate load capacity, etc. In this article, a method is suggested for modeling the masonry walls under in-plane loading. At the outset, a set of analytical equations was established for determining the elastic properties of an equivalent homogeneous material of masonry. The results for homogenized unreinforced brick walls through detailed modeling were compared in different manners such as solid and perforated walls, in-plane and out-of-plane loading, etc, and it was found that this method provides suitable accuracy in estimation of the wall linear properties. Furthermore, comparison of the results of proposed modeling with experimental out coming indicated that this model considers the non linear properties of the wall such as failure pattern, performance curve and ultimate strength, and would be appropriate to establish a parametric study on those prone factors. The proposed model is complicated; therefore, efforts need to be made in order to overcome the convergency problems which will be included in this study. The nonlinear model is basically semi-macro but through a series of actions, it can be simplified to a macro model.

Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method

  • Tahouneh, Vahid
    • Structural Engineering and Mechanics
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    • v.52 no.4
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    • pp.663-686
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    • 2014
  • This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

NONLINEAR OUTPUT VOLTAGE CONTROLOF PWM DC-DC CONBERTERS BY FEEDBACK LINERIZATION

  • Jo, Byeong-Rim;Min, Byung-Hoon;Choi, Hang-June
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.223-226
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    • 1995
  • New output voltage control technique based on the simple feedback linearization is proposed. The system states are first divided into fast states and slow states. Then, the control stage is composed of the fast inner current control loop and the slow outer voltage control loop. From the inner loop, the average control is derived by the sliding mode concept and it is inserted into the dynamic equations of the slow states in the outer loop. Applying the feedback linearization technique to the obtained large-signal models of the PWM dc-dc converters, linearized large-signal models are obtained for the slow states. With this technique, the output voltage controller of the PWM dc-dc converters can be designed easily in the global state space and its control performance can also be much improved.

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Design and Field Test of Heading and Depth Control Based on PD Control of Torpedo Type AUV, HW200 (PD제어 기법을 적용한 어뢰형 무인잠수정(HW200)의 선수각 및 심도제어기 설계와 실해역 성능 검증)

  • Park, Sung-kook;Lee, Phil-yeop;Park, Sangwoong;Kwon, Soon T.;Jung, Hunsang;Park, Min-su
    • Journal of Institute of Control, Robotics and Systems
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    • v.21 no.10
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    • pp.951-957
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    • 2015
  • This Paper considers the heading and depth control problem for an underactuated AUV (Autonomous Underwater Vehicle) HW200. The HW200 is a torpedo-type AUV that is developed from Hanwha corporation R&D Center for military operation such as MCM (Mine Counter Measures). The HW200 controls horizontal and vertical motion with two stern plane and two rudder plane. It is well known that fine control of an AUV motion is not easy because of model uncertainties, highly nonlinear and coupled motions. To overcome those kind of uncertainties, a number of control methods have been presented. In this paper, the motion controllers of the HW200 are designed using PD controller design method based on the linear and perturbed model of the typical 6-DOF equations of an AUV, and confirmed the effectiveness of the controller through simulations and field test.