• Title/Summary/Keyword: Euler beam theory

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Stability Analysis of Cracked Cantilever Beam Subjected to Follower Force (종동력을 받는 크랙 외팔 보의 안정성 해석)

  • Ahn, Sung-Jin;Yoon, Han-Ik;Son, In-Soo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.215-218
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    • 2007
  • In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam subjected to follower force is presented. In addition, an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter insstability based on the variation of the first two resonant frequencies of the beam. Besides, the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

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Wave propagation of a functionally graded beam in thermal environments

  • Akbas, Seref Doguscan
    • Steel and Composite Structures
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    • v.19 no.6
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    • pp.1421-1447
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    • 2015
  • In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

Stability Analysis of Cracked Cantilever Beam With Tip Mass and Follower Force (끝단질량과 종동력을 가진 크랙 외팔 보의 안정성 해석)

  • Yoon, Han-Ik;Son, In-Soo;Ahn, Tae-Su
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.99-104
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    • 2007
  • In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam with tip mass and follower force is presented. In addition. an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter ins stability based on the variation of the first two resonant frequencies of the beam. Besides. the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

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Adaptive control for two-link flexible robot arm (2-링크 유연한 로보트 팔에 대한 적응제어)

  • 한종길;유병국;임규만;함운철
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10a
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    • pp.8-13
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    • 1993
  • This paper presents deterministic and adaptive control laws for two-link flexible arm. The flexible arm has considerable structural flexibility. Because of its flexbility, dynamic equations are very complex and difficult to get, dynamic equations for two-link flexible arm are derived from Bernoulli-Euler beam theory and Lagrangian equation. Using the fact that matrix is skew symmetric, controllers which have a simplified structure with less computational burden are proposed by using Lyapunov stability theory.

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Semi-analytical stability behavior of composite concrete structures via modified non-classical theories

  • Luxin He;Mostafa Habibi;Majid Khorami
    • Advances in concrete construction
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    • v.17 no.4
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    • pp.187-210
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    • 2024
  • Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

On the static stability of nonlocal nanobeams using higher-order beam theories

  • Eltaher, M.A.;Khater, M.E.;Park, S.;Abdel-Rahman, E.;Yavuz, M.
    • Advances in nano research
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    • v.4 no.1
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    • pp.51-64
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    • 2016
  • This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.

Analysis of Lamb wave propagation on a plate using the spectral element method (스펙트럼 요소법을 이용한 판 구조물의 램파 전달 해석)

  • Lim, Ki-Lyong;Kim, Eun-Jin;Choi, Kwang-Kyu;Park, Hyun-Woo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2008.11a
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    • pp.71-81
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    • 2008
  • This paper proposes a spectral element which can represent dynamic responses in high frequency domain such as Lamb waves on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by piezoelectric layer (PZT layer) bonded on a base plate. In the two layer beam model, a PZT layer is assumed to be rigidly bonded on a base beam. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with electro mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are formulated through equations of motions converted into frequency domain. A detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through comparison results with the conventional 2-D FEM and the previously developed spectral elements.

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Identification of beam crack using the dynamic response of a moving spring-mass unit

  • An, Ning;Xia, He;Zhan, Jiawang
    • Interaction and multiscale mechanics
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    • v.3 no.4
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    • pp.321-331
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    • 2010
  • A new technique is proposed for bridge structural damage detection based on spatial wavelet analysis of the time history obtained from vehicle body moving over the bridge, which is different from traditional detection techniques based on the bridge response. A simply-supported Bernoulli-Euler beam subjected to a moving spring-mass unit is established, with the crack in the beam simulated by modeling the cracked section as a rotational spring connecting two undamaged beam segments, and the equations of motion for the system is derived. By using the transfer matrix method, the natural frequencies and mode shapes of the cracked beam are determined. The responses of the beam and the moving spring-mass unit are obtained by modal decomposition theory. The continuous wavelet transform is calculated on the displacement time histories of the sprung-mass. The case study result shows that the damage location can be accurately determined and the method is effective.

Effects of Crack and Tip Mass on Stability of Timoshenko Beam Subjected to Follower Force (종동력을 받는 티모센코 보의 안정성에 미치는 크랙과 끝질량의 영향)

  • Son, In-Soo;Yoon, Han-Ik;Ahn, Tae-Soo
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.6
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    • pp.99-107
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    • 2008
  • In this paper, the stability of a cracked cantilever Timoshenko beam with a tip mass subjected to follower force is investigated. In addition, an analysis of the flutter instability(flutter critical follower force) and a critical natural frequency of a cracked cantilever Euler / Timoshenko beam with a tip mass subjected to a follower force is presented. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Therefore, the effect of the crack's intensity, location and a tip mass on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

Free Vibration Analysis of Simply Supported Beam with Double Cracks (이중크랙을 가진 단순지지 보의 자유진동 해석)

  • Ahn, Sung-Jin;Son, In-Soo;Yoon, Han-Ik
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.600-603
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    • 2005
  • In this paper we studied about the effect of the double cracks on the dynamic behavior of a simply supported beam. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The simply supported beam is modeled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack depth and position of each crack on the vibration mode and the natural frequencies of a simply supported beam are analytically clarified. The theoretical results are also validated by a comparison with experimental measurements.

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