• Proceedings of the KSR Conference
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• 2007.11a
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• pp.107-114
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• 2007

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Journal of Industrial Technology
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• v.19
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• pp.227-233
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• 1999

Simple equations which can predict "exact" values of the natural frequency of vibration for the special orthotropic laminates are presented. Many laminates with certain orientations have decreasing values of $B_{16}$ and $B_{26}$ as the number of plies increases. Such laminates, with $D_{16}=D_{26}{\rightarrow}0$, including the laminates with anti-symmetric configurations can be solved by the same equation for the special orthotropic laminates. If the quasi-isotropic constants are used, the equations for the isotropic plates can be used. Use of some coefficients cab produce "exact" value for laminates with such configurations. Natural frequencies of the plate with varying aspect ratios is presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.318-324
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• 2004

The stability of a simply supported straight pipe is investigated. The time dependent flow is assumed to vary harmonically about a constant mean velocity. Stability conditions and dynamic reponses of a governing equation are conducted by use of multiple scale mettled. Parametric resonances and combination resonances are investigated. Stability boundaries are analytically determined. The resulted stability conditions show that instabilities exist when the frequency of flow fluctuation is close to two times the natural frequency or to the sum of any two natural frequencies. In case that the fluctuated flow frequency is close to zero or to the difference of two natural frequencies, however, instabilities are not found up to the first order of perturbation. Stability charts are numerically Presented fir the first two vibration modes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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• pp.1053-1059
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• 2005

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.4
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• pp.323-330
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• 2010

An efficient wave energy converter with new overtopping flow device on which spiral reefs are attached is proposed by Maritime and Ocean Engineering Research Institute in Korea and its candidate substructures such as monopile, tripod and jacket are designed. This study investigates modal characteristics of the substructures by analyzing natural frequencies and mode shapes. Based on the modal analysis results, relative strength, governing modes and some complementary design strategies of each candidate substructure are compared and discussed considering water depth conditions.

• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.481-506
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• 2009

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.501-508
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• 2001

Free vibration analysis of multi-delaminated composite beam-columns subjected to axial compression load is performed in the present study. In order to investigate the effects of multi-delaminations on the natural frequency and elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. Characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and elastic buckling load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.11-16
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• 2002

The differential equations governing free vibrations of the elastic, horizontally curved beams with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates, in which the effect of torsional inertia is included. Frequencies are computed numerically for the sinusoidal curved beams with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without torsional inertia, as functions of three non-dimensional system parameters: the horizontal rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.215-222
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• 1997

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross-sections and with arbitrary boundary conditions was developed and reported by D. H. Kim in 1974. This method has been developed for two-dimensional problems including the laminated composite plates and was proved to be very effective for the plates with arbitrary boundary conditions and irregular sections. In this paper, the result of application of this method to the subject problem is presented. This problem represents the building slabs with a kind of passive and active control devices. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation on the natural frequency is thoroughly studied.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05a
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• pp.335-338
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• 2005

This study was performed to verify that the impact vibration test on the damaged concrete pier can be adopted for assessment of the bridge substructure integrity. Using the experimental modal analysis, the dynamic property changes of the concrete pier are investigated according to the damage levels which are modeled by the loss of cross section area of the pier body. As a result of the impact vibration test, it is found that the natural frequency of the bridge substructure is reduced due to the damage on the pier such as loss of cross section area, and the natural frequency can be used for assessment of the integrity index.