• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.799-804
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• 2004

In this paper a dynamic behavior of simply supported cracked simply supported beam with the moving masses is presented. Based on the Timoshenko beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics the of. And the crack is assumed to be in th first mode of fracture. As the depth of the crack and velocity of fluid are increased the mid-span deflection of the pipe conveying fluid with the moving mass is increased. As depth of the crack is increased, the effect that the velocity of the fluid on the mid-span deflection appeals more greatly.

• Journal of KSNVE
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• v.8 no.4
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• pp.616-622
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• 1998

An analytical method has been developed to estimate the dynamic contact force between wheel and rail when trains are running on rail with vertical irregularities. In this method, the effect of Hertzian deformation at the contact point is considered as a linearized spring and the wheel is considered as an sprung mass. The rail is modelled as a discretely-supported Timoshenko beam, and the periodic structure theory was adopted to obtain the driving-point receptance. As an example, the dynamic contact force for a typical wheel/rail system was analysed by the method developed in this research and the dynamic characteristics of the system was also discussed. It is revealed that discretely-supported Timoshenko beam model should be used instead of the previously used continuously-supported model or discretelysupported Euler beam model, for the frequency range above several hundred hertz.

• Steel and Composite Structures
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• v.26 no.6
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• pp.733-743
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• 2018

This paper presents post-buckling responses of a simply supported laminated composite beam subjected to a non-follower axially compression loads. In the nonlinear kinematic model of the laminated beam, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The distinctive feature of this study is post-buckling analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. The effects of the fibber orientation angles and the stacking sequence of laminates on the post-buckling deflections, configurations and stresses of the composite laminated beam are illustrated and discussed in the numerical results. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the laminated composite beams.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.8
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• pp.11-16
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• 1998

Recently, the motor-integrated spindle systems have been used to simplify the machine tool structure, to improve the motion flexibility of machine tool, and to perform the high-speed machining. In this study, a static and dynamic analysis system for motor-integrated high-speed spindle systems is developed based on Timoshenko theory, finite element method and windows programming techniques. Since the system has various analysis modules related to static deformation analysis, modal analysis, frequency response analysis, unbalance response analysis and so on, it is useful in performing systematically the design and evaluation processes of motor-integrated high-speed spindle systems under windows GUI environment.

• Structural Engineering and Mechanics
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• v.34 no.2
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• pp.231-245
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• 2010

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

• Coupled systems mechanics
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• v.7 no.6
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• pp.691-705
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• 2018

In this paper, nonlinear displacements of laminated composite beams are investigated under non-uniform temperature rising with temperature dependent physical properties. Total Lagrangian approach is used in conjunction with the Timoshenko beam theory for nonlinear kinematic model. Material properties of the laminated composite beam are temperature dependent. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The distinctive feature of this study is nonlinear thermal analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. In this study, the differences between temperature dependent and independent physical properties are investigated for laminated composite beams for nonlinear case. Effects of fiber orientation angles, the stacking sequence of laminates and temperature on the nonlinear displacements are examined and discussed in detail.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.285-287
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• 2014

Equations of motion for the vibration analysis of rotating pre-twisted beams with functionally graded material properties are derived in this paper. Based on Timoshenko beam theory, the effects of shear and rotary inertia are considered. The pre-twisted beam has a rectangular cross-section and is mounted on a rotating rigid hub with a setting angle. Functionally graded material (FGM) properties are considered along the height direction of the beam. The equations of stretching and bending motion are derived by Kane's method employing hybrid deformation variables. To validate the derived equations, natural frequencies of a rotating FGM pre-twisted beam are compared to those obtained by a commercial software ANSYS. The effects of the pre-twisted angle, slenderness ratio, hub radius, volume fraction exponent, and angular speed on the modal characteristics of the system are investigated with the proposed model.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Smart Structures and Systems
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• v.17 no.5
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• pp.837-857
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• 2016

In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen's nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton's principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.223-233
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.