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  • Title/Summary/Keyword: Euler-beam theory

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Study on Method of Crack Detection of L-beams with Coupled Vibration (연성진동하는 L형 단면 보의 크랙 검출 방법에 대한 연구)

  • Son, In-Soo;Cho, Jeong-Rae;Ahn, Sung-Jin
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.9 no.6
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    • pp.78-86
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    • 2010
  • This paper aims to investigate the natural frequency of a cracked cantilever L-beams with a coupled bending and torsional vibrations. In addition, a theoretical method for detection of the crack position and size in a cantilever L-beams is presented based on natural frequencies. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using extended Hamilton's Principle. The dynamic transfer matrix method is used for calculation of a exact natural frequencies of L-beams. In order to detect the crack of L-beams, the effect of spring coefficients for bending moment and torsional force is included. In this study, the differences between the actual data and predicted positions and sizes of crack are less than 0.5% and 6.7% respectively.

Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler-Pasternak elastic medium

  • Cetin, Dogan;Simsek, Mesut
    • Structural Engineering and Mechanics
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    • v.40 no.4
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    • pp.583-594
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    • 2011
  • In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)

  • Bilouei, Babak Safari;Kolahchi, Reza;Bidgoli, Mahmood Rabani
    • Computers and Concrete
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    • v.18 no.5
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    • pp.1053-1063
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    • 2016
  • As concrete is most usable material in construction industry it's been required to improve its quality. Nowadays, nanotechnology offers the possibility of great advances in construction. For the first time, the nonlinear buckling of straight concrete columns armed with single-walled carbon nanotubes (SWCNTs) resting on foundation is investigated in the present study. The column is modelled with Euler-Bernoulli beam theory. The characteristics of the equivalent composite being determined using the Mori-Tanaka model. The foundation around the column is simulated with spring and shear layer. Employing nonlinear strains-displacements, energy methods and Hamilton's principal, the governing equations are derived. Differential quadrature method (DQM) is used in order to obtain the buckling load of structure. The influences of volume percent of SWCNTs, geometrical parameters, elastic foundation and boundary conditions on the buckling of column are investigated. Numerical results indicate that reinforcing the concrete column with SWCNTs, the structure becomes stiffer and the buckling load increases with respect to concrete column armed with steel.

A Study on the Position Control Improvement of Flexible Robot Arm by Inverse Dynamics (역학을 이용한 탄성 로보트 아암의 선단 위치 제어 기어에 대한 연구)

  • 방두열;이성철
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1997.04a
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    • pp.9-13
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    • 1997
  • This parer is a study on the inverse dynamics of a one-link flexible robot arm which is controlled by translational base motion. The system is composed of a flexible arm, a base for driving arm, a DC servomotor, and a computer. The arm base is moved so that the arm tip follows a desired function. The governing equations are based on the Bernoullie-Euler beam theory and solved by applying the Laplace transform method and then the numerical inversion method. Moter voltage is obtained by simulation for tip trajectory functions i. e. Bang-Bang, Cosine and Gauss Function. And, the tip motion is measured while simulation results are applying. Then the results are investigated to select most proper input and to compare their chateristics. Experimental results show the Cosine function is most proper with respect to low maximum voltage and steady state error.

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Effects of Crack on Stability of Cantilever Pipe Conveying Fluid (유체유동 외팔 파이프의 안정성에 미치는 크랙의 영향)

  • Son, In-Soo;Yoon, Han-Ik;Kim, Dong-Jin
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.11
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    • pp.1119-1126
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    • 2007
  • In this paper, the dynamic stability of a cracked cantilever pipe conveying fluid with tip mass is investigated. The pipe is modelled by the Euler-Bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored. The equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influence of the crack severity, the position of crack, the mass ratio, and a tip mass on the stability of a cantilever pipe conveying fluid are studied by the numerical method. Besides, the critical flow velocity and the stability maps of the pipe system as a function of mass ratios(β) for the changing each parameter are obtained.

Static and dynamic stability of cracked multi-storey steel frames

  • Sabuncu, Mustafa;Ozturk, Hasan;Yashar, Ahmed
    • Structural Engineering and Mechanics
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    • v.58 no.1
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    • pp.103-119
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    • 2016
  • Multi-storey frame structures are frequently exposed to static and dynamic forces. Therefore analyses of static (buckling) and dynamic stability come into prominence for these structures. In this study, the effects of number of storey, static and dynamic load parameters, crack depth and crack location on the in-plane static and dynamic stability of cracked multi-storey frame structures subjected to periodic loading have been investigated numerically by using the Finite Element Method. A crack element based on the Euler beam theory is developed by using the principles of fracture mechanics. The equation of motion for the cracked multi-storey frame subjected to periodic loading is achieved by Lagrange's equation. The results obtained from the stability analysis are presented in three dimensional graphs and tables.

Buckling of plates including effect of shear deformations: a hyperelastic formulation

  • Musa, Idris A.
    • Structural Engineering and Mechanics
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    • v.57 no.6
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    • pp.1107-1124
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    • 2016
  • Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

Free vibration analysis of continuous bridge under the vehicles

  • Tan, Guojin;Wang, Wensheng;Jiao, Yubo;Wei, Zhigang
    • Structural Engineering and Mechanics
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    • v.61 no.3
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    • pp.335-345
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    • 2017
  • Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

Thermal stability analysis of temperature dependent inhomogeneous size-dependent nano-scale beams

  • Bensaid, Ismail;Bekhadda, Ahmed
    • Advances in materials Research
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    • v.7 no.1
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    • pp.1-16
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    • 2018
  • Thermal bifurcation buckling behavior of fully clamped Euler-Bernoulli nanobeam built of a through thickness functionally graded material is explored for the first time in the present paper. The variation of material properties of the FG nanobeam are graded along the thickness by a power-law form. Temperature dependency of the material constituents is also taken into consideration. Eringen's nonlocal elasticity model is employed to define the small-scale effects and long-range connections between the particles. The stability equations of the thermally induced FG nanobeam are derived via the principal of the minimum total potential energy and solved analytically for clamped boundary conditions, which lead for more accurate results. Moreover, the obtained buckling loads of FG nanobeam are validated with those existing works. Parametric studies are performed to examine the influences of various parameters such as power-law exponent, small scale effects and beam thickness on the critical thermal buckling load of the temperature-dependent FG nanobeams.

Dynamic Stability Analysis of Tapered Beck Columns (변단면 Beck 기둥의 동적안정 해석)

  • Lee Byoung-Koo;Lee Tae-Eun;Kang Hee-Jong;Kim Gwon-Sik
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2006.04a
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    • pp.949-954
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    • 2006
  • The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.

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