• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.303-314
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• 2004

An artificial neural network (ANN) application is presented for flexural and axial vibration analysis of elastic beams with various support conditions. The first three natural frequencies of beams are obtained using multi layer neural network based back-propagation error learning algorithm. The natural frequencies of beams are calculated for six different boundary conditions via direct solution of governing differential equations of beams and Rayleigh's approximate method. The training of the network has been made using these data only flexural vibration case. The trained neural network, however, had been tested for cantilever beam (C-F), and both end free (F-F) in case the axial vibration, and clamped-clamped (C-C), and Guided-Pinned (G-P) support condition in case the flexural vibrations which were not included in the training set. The results found by using artificial neural network are sufficiently close to the theoretical results. It has been demonstrated that the artificial neural network approach applied in this study is highly successful for the purposes of free vibration analysis of elastic beams.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.1-4
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• 2001

Dynamic analysis of laminated beams with a embedded damping layer under tension or compression axial load is investigated. Improved Layer-Wise Zig-Zag Beam Theory and Interdependent Kinematic Relation using the governing equations of motion are incorporated to model the laminated beams with a damping layer and a corresponding beam zig-zag finite element is developed. Flexural frequencies and modal loss actors under tension or compression axial load are calculated based on Complex Eigenvalue Method. The effect of the axial tension and compression load on the frequencies and loss factors is discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.598-604
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• 2003

In order to meet the growing demands for higher storage density as well as lower noise level, the spindles In hard disk drives are to be supported by hydrodynamic bearings in place of conventional ones. However, the existing models are inappropriate to apply to accurate Prediction or vibration characteristics because the Inn spindle tends to take quite a complex shape to secure the performance of the new type bearings. In this context, this paper treats analysis of free and forced vibrations of such-designed HDD spindles based on more sophisticated models and validation by means of experiments. Remarkably, to this end each component in the system is modeled as elastic adopting the finite element method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.11
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• pp.852-859
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• 2003

In order to meet the growing demands for higher storage density as well as lower noise level, the spindles in hard disk drives are to be supported by hydrodynamic bearings in place of conventional ball-type ones. However, the existing models are inappropriate to apply to accurate prediction of vibration characteristics because the HDD spindle tends to take quite a complex shape to secure its performance and cost-effectiveness. In this context, this paper treats analysis of free and forced vibrations of such-designed HDD spindles based on more sophisticated models and validations via experiments. Remarkably, to this end all the components in the system are modeled as elastic adopting the finite element method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.4
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• pp.64-69
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• 2002

Dynamic analysis of laminated beams with a embedded damping layer under tension or compression axial load is investigated. Improved Layer-Wise Zig-Zag Beam Theory and Interdependent Kinematic Relation using the governing equations of motion are incorporated to model the laminated beams with a damping layer and a corresponding beam zig-zag finite element is developed. Flexural frequencies and modal loss factors under tension or compression axial load are calculated based on Complex Eigenvalue Method. The effects of the axial tension and compression load on the frequencies and loss factors are discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.192-199
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• 2002

The use of frequency-dependent dynamic stiffness matrix (or spectral element matrix) in structural dynamics may provide very accurate solutions, while it reduces the number of degrees-of-freedom to improve the computational efficiency and cost problems. Thus, this paper develops a spectral element model for the thin plates moving with constant speed under uniform in-plane tension. The concept of Kantorovich method is used in the frequency-domain to formulate the dynamic stiffness matrix. The present spectral element model is evaluated by comparing its solutions with the exact analytical solutions. The effects of moving speed and in-plane tension on the flexural wave dispersion characteristics and natural frequencies of the plate are numerically investigated.

• Journal of the Korean Society for Advanced Composite Structures
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• v.6 no.2
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• pp.97-104
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• 2015

Compared with a strong axial rigidity due to large intial tension, cable has a weak laterally flexural rigidity. A variety of dynamic loads such as traffic loads and wind loads etc. cause the cables to vibrate significantly and affect the mechanical properties and the performance of cables. Therefore, vibration reduction design is an urgent task to control the vibration of cable-supported bridges. Because a various kind of dampers have shown to reduce the amplitude and duration time of vibration of cable from measured date in field test, damper can be considered that it is effective device significantly to reduce the amplitude and duration time in vibration of cable. Vibration characteristics of cable can change according to manufacturing method and type of established form, and damper has been designed according to distribution of natural frequencies and vibration modes. In this study, numerical analysis is used to show the reduction effects of vibrations and present the design of damper for vibration reduction of cable.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.6 s.99
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• pp.749-756
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• 2005

This paper presents vibration analyses of hard disk drive (HDD) spindle systems based on the finite element method. The systems under investigation have a cantilevered shaft rotating on hydrodynamic bearings. In particular, the influence of stator's flexibility on major modes has been taken into account in dual ways lumped and distributed-parameter model approfches. Even the latter employs relatively macroscopic elements instead of extremely fine ones Popular in commercial codes. In order to prove the effectiveness of such formulated models, two types of HDD prototypes featuring different hub and stator structures are selected as examples. Compared to the first, the second type has a reinforced stator that would raise the natural frequency of the hub's translational (or sideway) mode. Both free and forced vibration characteristics are computed, and subsequently compared with the experimental data. It is our conclusion that Particularly the Proposed distributed model method is an efficient design tool for state-of-the-art HDD spindle systems.