• Title/Summary/Keyword: Euler-beam theory

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Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core

  • Sudhakar, V;Gopalkrishnan, S;Vijayaraju, K
    • Structural Engineering and Mechanics
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    • v.65 no.6
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    • pp.657-678
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    • 2018
  • Sandwich structures are well known for their use in aircraft, naval and automobile industries due to their high strength resistance with light weight and high energy absorption capability. Sandwich beams with soft core are very common and simple structures that are employed in day to day general use appliances. Modeling and analysis of sandwich structures is not straight forward due to the interactions between core and face sheets. In this paper, formulation of Super Convergent finite elements for analysis of the sandwich beams with soft core based on Euler Bernoulli beam theory are presented. Two elements, Eul4d with 4 degrees of freedom assuming rigid core in transverse direction and Eul10d with 10 degrees of freedom assuming the flexible core were developed are presented. The formulation considers the top, bottom face sheets and core as separate entities and are coupled by beam kinematics. The performance of these elements are validated by results available in the published literature. Number of studies are performed using the formulated elements in static, free vibration and wave propagation analysis involving various boundary and loading conditions. The paper highlights the advantages of the elements developed over the traditional elements for modeling of sandwich beams and, in particular wave propagation analysis.

Theoretical Analysis of Carbon Nanotube Actuators (탄소나노튜브 작동기의 이론적 해석)

  • Park C.H.;Park H.C.;So H.K.;Jung B.B.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2005.06a
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    • pp.927-931
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    • 2005
  • Carbon nanotube actuator, working under physical conditions (in aqueous solution) and converting electrical energy into mechanical energy directly, can be a good substitute for artificial muscle. The carbon nanotube actuator simulated in this paper is an isotropic cantilever type with an adhesive tape which is sandwiched between two single-walled carbon nanotubes. For predicting the static and dynamic characteristic parameters, the analytical model for a 3 layer bimorph carbon nanotube actuator is developed by using Euler-Bernoulli beam theory. The governing equation and boundary conditions are derived from energy principles. The induced displacements of the theoretical model are presented in order to investigate the performance of the carbon nanotube actuator with different control voltages. The developed model presents invaluable means for designing and predicting the performance of carbon nanotube actuator that can be used in artificial muscle applications.

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Surface effects on flutter instability of nanorod under generalized follower force

  • Xiao, Qiu-Xiang;Zou, Jiaqi;Lee, Kang Yong;Li, Xian-Fang
    • Structural Engineering and Mechanics
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    • v.64 no.6
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    • pp.723-730
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    • 2017
  • This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

Analytical Modeling of Carbon Nanotube Actuators (탄소나노튜브 액츄에이터의 이론적 모델링)

  • 염영일;박철휴
    • Journal of Institute of Control, Robotics and Systems
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    • v.10 no.11
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    • pp.1006-1011
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    • 2004
  • Carbon nanotubes have outstanding properties which make them useful for a number of high-technology applications. Especially, single-walled carbon nanotube (SWNT), working under physical conditions (in aqueous solution) and converting electrical energy into mechanical energy directly, can be a good substitute for artificial muscle. The carbon nanotube structure simulated in this paper is an isotropic cantilever type with an adhesive tape which is sandwiched between two SWNTs. For predicting the geometrical and physical parameters such as deflection, slope, bending moment and induced force with various applied voltages, the analytical model for a 3 layer bimorph nanotube actuator is developed by applying Euler-Bernoulli beam theory. The governing equation and boundary conditions are derived from energy Principles. Also, the brief history of carbon nonotube is overviewed and its properties are compared with other functional materials. Moreover, an electro-mechanical coupling coefficient of the carbon nanotube actuator is discussed to identify the electro-mechanical energy efficiency.

Buckling oad and Post-buckling Behavior of Tapered Column with Constant Volume and Both Clamped Ends (일정체적 양단고정 변단면 기둥의 좌굴하중 및 후좌굴 거동)

  • 이병구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.41 no.5
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    • pp.112-122
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    • 1999
  • 이 논문은 일정체적을 갖는 양단고정 변단면 기둥의 좌굴하중 및 후좌굴 거동에 관한 연구이다. 기둥의 변단면으로는 직선형, 포물선형, 정현의 선형을 갖는세 가지 변단면을 채택하였다. Bernoulli-Euler 보 이론을 이용하여 압축하중이 작용하여 좌굴된 기둥이 정확탄성곡선을 지배하는 미분방정식을 유도하였다. 유도된 미분방정식을 Runge-Kutta 법과 REgula-Falsi법을 이용하여 수치해석하였다. 수치해석의 결과로 좌굴하중, 좌굴기둥의 평형경로 및 정확탄성곡선을 산출하였다. 또한 좌굴하중-단면비 곡선으로부터 최강기둥의 좌굴하중과 단면비를 산출하였다.

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Critical buckling loads of carbon nanotube embedded in Kerr's medium

  • Bensattalah, Tayeb;Bouakkaz, Khaled;Zidour, Mohamed;Daouadji, Tahar Hassaine
    • Advances in nano research
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    • v.6 no.4
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    • pp.339-356
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    • 2018
  • In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.

Design of the controller with sliding mode for flexible robot arm (유연한 로봇 팔의 슬라이딩모드를 갖는 제어기 설계)

  • 김성태;임규만;함운철
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.547-551
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    • 1996
  • In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagrangian assumed modes method based on Bernoulli-Euler Beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoption of a continuous control law within a small neighborhood of the switching hyperplane.

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Design of the Controller with Sliding Mode for Robot Arm (슬라이딩모드를 갖는 로봇 팔의 제어기 설계)

  • 서원창;임규만;정영창
    • Proceedings of the IEEK Conference
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    • 1999.11a
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    • pp.703-706
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    • 1999
  • In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagragian assumed modes method based on Bernoulli-Euler beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoptation of a continuous control law within a small neighborhood of the switching hyperplane.

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Microstructure and Impactive Flexural Vibration Characteristics of Glass-Fabric/Epoxy Composite Beams (유리직물/에폭시 복합재료 보의 내부구조와 충격굽힘진동특성)

  • 서지웅;최낙삼
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 1999.04a
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    • pp.53.1-56
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    • 1999
  • The vibration behavior of glass-fabric reinforced plastic(GFRP) composite beams subjected to various transverse impacts has been investigated as a function of fiber orientation and void fraction. Theoretical results of resonant frequency damping coefficient and modal amplitude dispersion using the Euler-beam theory were obtained along with the finite element analysis which were compared with experimental ones Consequently it was shown that the transverse vibration characteristics were largely affected by fiber orientation and void fraction.

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Forced Vibration of Elastically Restrained Valve-pipe System (탄성지지된 밸브 배관계의 강제진동 특성)

  • Son, In-Soo;Hur, Kwan-Do
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2011.04a
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    • pp.679-680
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    • 2011
  • The Forced vibration characteristics of elastically restrained pipe conveying fluid with the attached mass are investigated in this paper. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Hamilton's principle. The effect of attached mass and spring constant on forced vibration of pipe system is studied. Also, the critical flow velocities and stability maps of the valve-pipe system are obtained as each parameters.

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