• Title/Summary/Keyword: Governing equation

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Free axial vibration of cracked axially functionally graded nanoscale rods incorporating surface effect

  • Nazemnezhad, Reza;Shokrollahi, Hassan
    • Steel and Composite Structures
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    • v.35 no.3
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    • pp.449-462
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    • 2020
  • This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

Large Deflection of a Viscoelastic Beam (점탄성 물질로 만들어진 보의 대변형 해석)

  • Lee, Kyung-Woo
    • Textile Science and Engineering
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    • v.42 no.5
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    • pp.284-287
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    • 2005
  • The governing equation for a large deflection of linear viscoelastic beam is derived. Because of the complexity involved in the governing equation that is a nonlinear integro-differential equation, solutions were obtained by numerical approximations for the case of the cantilever beam under a concentrated load and a combined load.

Longitudinal Vibration Analysis of Deploying Rods (전개하는 막대의 종진동 해석)

  • Cho, Eun-Hyoung;Chung, Jin-Tai
    • Proceedings of the KSME Conference
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    • pp.625-630
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    • 2000
  • In this paper, the governing equation and the boundary conditions of deploying rods are derived by using Hamilton's principle. The Galerkin method using the comparison function of the instantaneous natural modes is adopted by which the governing equation is discretized. Based on the discretized equations, the time integration analysis is performed and the longitudinal vibrations for the deploying and the retrieving velocity are analyzed.

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Redistribution of Vacancy Concentration in Metal Specimens under Stress-induced Diffusion at a High Temperature (고온 환경하 응력 확산에 의한 금속시편내 격자결함 재분포)

  • Yoon, Seon-Jhin;Cho, Yong-Moo
    • Journal of the Korea Society of Die & Mold Engineering
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    • v.12 no.1
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    • pp.1-6
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    • 2018
  • In this study, we calculated the redistribution of vacancy concentration in metal specimens induced by stress-induced diffusion at a high temperature. To deduce the governing equation, we associated the unit volume change equation of strains with a differential equation of vacancy concentration as a function of stress using the stress-strain relationship. In this governing equation, we considered stress as the only chemical potential parameter to stay in the scope of this study, which provided the vacancy concentration equation as of stress gradient in metals. The equation was then mathematically delineated to derive a analytical solution for a transient, one-dimensional diffusion case. With the help of Korhonen's approximation and the boundary conditions, we successfully deduced a general solution from the governing equation. To visualize the feasibility of our solutions, we applied the solution to two different stress-induced cases - a rod with fixed concentrated stresses at both ends and a rod with varying concentrated stresses at both ends. Although it is necessary to legitimatized the model in the future for improvement, our results showed that the model can be used to interpret the location of structural defects, the formation of vacancy, and furthermore the high temperature behavior of metals.

Flow and Displacement of Non-Newtonian Fluid(Power-Law Model) by Surface Tension and Gravity Force in Inclined Circular Tube (경사진 원형관에서 표면장력과 중력에 의한 비뉴턴 유체(멱법칙 모델)의 유동 및 변위)

  • Moh, Jeong Hah;Cho, Y.I.
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.38 no.1
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    • pp.9-16
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    • 2014
  • This paper presents the theoretical analysis of a flow driven by surface tension and gravity in an inclined circular tube. A governing equation is developed for describing the displacement of a non-Newtonian fluid(Power-law model) that continuously flows into a circular tube owing to surface tension, which represents a second-order, nonlinear, non-homogeneous, and ordinary differential form. It was found that quantitatively, the theoretical predictions of the governing equation were in excellent agreement with the solutions of the equation for horizontal tubes and the past experimental data. In addition, the predictions compared very well with the results of the force balance equation for steady.

Analysis of Water Surface Oscillation in the Surge Tank Due to the Variation of Water Level (수위변화에 따른 조압수조 내 수면진동에 대한 분석)

  • Jun, Kye-Won;Lee, Ho-Jin;Park, Jae-Sung;An, Sang-Do;Yoon, Young-Ho
    • 한국방재학회:학술대회논문집
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    • pp.441-444
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    • 2007
  • Surge tank generally are used near the downstream end of tunnels of penstocks to reduce change in pressure caused by waterhammer resulting from load changes on the turbines. In this paper, the surge tank with chamber is selected to analyze water surface oscillation. the governing equation are derived using the law of conservation of mass and momentum. the water surface oscillation in the surge tank are computed using governing equation. In the case of upsurging, water surface oscillation is damped gradually and in the case of downsurging, it is damped rapidly.

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End-point position control of a flexible arm by PID self-tuning fuzzy controller

  • Yang, G.T.;Ahn, S.D.;Lee, S.C.;Chonan, S.;Inooka, H.
    • 제어로봇시스템학회:학술대회논문집
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    • pp.496-500
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    • 1993
  • This paper presents an end-point position control of 1-link flexible robot arm by the PID self-tuning fuzzy algorithm. The governing equation is derived by the extended Hamilton's principle and based on the Bernoullie-Euler beam theory. The governing equation is solved by applying the Laplace transform and the numerical inversion method. The arm is mounted on the translational mechanism driven by a ballscrew whose rotation is controlled by dcservomotor. Tip position is controlled by the PID self-tuning fuzzy algorithm so that it follows a desired position. This paper shows the experimental and theoretical results of tip dispalcement, and also shows the good effects reducing the residual vibration of the end-point.

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Viscoelastic stress analysis of nonaxisymmetrically heated cylindrical tubes (비축대칭 열하중을 받는 원통튜브의 점탄성 응력해석)

  • 박진석;서금석;김종인
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.2
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    • pp.396-403
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    • 1991
  • A solution is presented for the computation of the elastic-creep stresses in a hollow cylinder subjected to nonaxisymmetric temperature distribution. The creep problem is treated by the Maxwell creep model. Laplace transformation is used for reformation of the governing equation of elastic problem and Hooke's law in a function of .gamma. , .theta. , and creep constant. The governing equation is set up using the Airy stress function which leads to the biharmonic equation. The solution is obtained by using Fourer series method and Laplace inverse method used to obtain the stress components which include the variation of time. This solution shows excellent agreement with Lamkin's and Boley & Weiner's solution. The viscoelastic stresses are also obtained for the fuel rob tube subjecting nonaxisymmetric thermal load.

Real-Time Simulation of Thin Rod

  • Choi, Min Gyu;Song, Oh-Young
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.7 no.4
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    • pp.849-859
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    • 2013
  • This paper proposes a real-time simulation technique for thin rods undergoing large rotational deformation. Rods are thin objects such as ropes and hairs that can be abstracted as one-dimensional structures. Development of a real-time physical model that can produce visually convincing animation of thin rods has been a challenging problem in computer graphics. We adopt continuum mechanics to formulate the governing equation, and develop a modal warping technique for rods to integrate the governing equation in real-time; This is a novel extension of the previous modal warping techniques developed for solids and shells. Experimental results show that the proposed method runs in real-time even for large meshes and it can simulate large bending and/or twisting deformations.