• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.384-391
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• 2011

This paper deals with free vibrations of the parabolic hollowed beam-columns with constant volume. The cross sections of beam-column taper are the hollowed regular polygons whose depths are varied with the parabolic functional fashion. Volumes of the objective beam-columns are always held constant regardless given geometrical conditions. Ordinary differential equation governing free vibrations of such beam-columns are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam-column parameters such as end constraints, side number, section ratio, thickness ratio and axial load are reported in tables and figures.

• Journal of Ocean Engineering and Technology
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• v.19 no.2 s.63
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• pp.1-11
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• 2005

In the present paper, the hydrodynamic properties of a Rahmen type flexible porous breakwater with dual fixed pontoon system interacting with obliquely or normally incident small amplitude waves are numerically investigated. This system is composed of dual vertical porous membranes hinged at the side edges of dual fixed pontoons, and a submerged horizontal membrane that both ends are hinged at the steel frames mounted pontoons. The dual vertical membranes are extended downward and hinged at bottom steal frame fixed into seabed. The wave blocking and dissipation mechanism and its effects of permeability, Rahmen type membrane and pontoon geometry, pretensions on membranes, relative dimensionless wave number, and incident wave headings are thoroughly examined.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.63-69
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• 2003

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effects of rotatory inertia and shear deformation as well as the effects of both vertical and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported. with and without the effects of rotatory inertia and shear deformation. as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio. the slenderness ratio and the stiffness parameter.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.423-428
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• 2002

A numerical method is presented to obtain natural frequencies and mode shapes of tapered beams with static deflections due to self-weight. The differential equation governing the free vibrations of beam taken into account the static deflection due to self-weight is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged and clamped-free end constraints are applied in the numerical examples. As the numerical results, the lowest three natural frequencies versus distributed slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with the effects of static deflection are presented in figures.

• Journal of KSNVE
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• v.9 no.5
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• pp.1012-1018
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• 1999

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Journal of KSNVE
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• v.9 no.6
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• pp.1193-1199
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• 1999

This paper deals with the free vibrations of circular curved beams with thin-walled cross-section. The differential equation for the coupled flexural-torsional vibrations of such beams with warping is solved numerically to obtain natural frequencies and mode shapes. The Runge-Kutta and determinant search methods, respectively, are used to solve the governing differential equation and to compute the eigenvalues. The lowest three natural frequencies and corresponding mode shapes are calculated for the thin-walled horizontally curved beams with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of opening angle of beam, warping parameter, and two different values of slenderness ratios are considered. Numerical results are compared with existing exact and numerical solutions by other methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.10 s.115
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• pp.1074-1081
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• 2006

This paper deals with the dynamic stability analysis of clamped-hinged columns with constant volume. Numerical methods are developed for solving natural frequencies and buckling loads of such columns, subjected to an axial compressive load. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are always held constant. Differential equations governing both free vibrations and buckled shapes of such columns are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. The numerical methods developed herein for computing natural frequencies and buckling loads are found to be efficient and robust. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are reported in figures and tables.

• Journal of KSNVE
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• v.3 no.4
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• pp.331-339
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• 1993

The main purpose of this paper is to present an analytical method for free vibration of arches with thickness varying in a discontinuous fashion. The ordinary differential equations governing the free vibration of these arches are derived as nondimensional forms including the effect of rotatory inertia. The governing equation are solved numerically for the circular and sinusoidal arches with hinged-hinged-hinged end clamped-clamped end constraints. As the numerical results, the effect of rotatory inertia on the natural frequencies is reported. The lowest four natural frequencies are presented as the functions of four nondimensional system parameters; the rise to span length ratio, the slenderness ratio, the section ratio and the ratio of discontinuous section.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.57-65
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• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.

• Earthquakes and Structures
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• v.11 no.1
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• pp.45-61
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• 2016

Structures with soft story irregularity have been seriously damaged in earthquakes. Therefore, the analysis of dynamic behavior of structures with soft story irregularity is of great value and relevance. In this study, a certain method will be used to discover the displacements and internal forces and to find out results about soft story irregularity. For this study, the multi-story frame-hinged shear wall system has been used as a model according to the continuous calculation system. The dynamic characteristics of the system have been obtained by analyzing the governing differential equation of the system. The dynamic characteristics have been calculated for a practical and quick analysis as indicated in tables. The suggested method is wholly based on manual calculation. A spectral analysis can be easily conducted with the help of Tables provided by this study. A sample has been solved and compared to the finite elements method to study the suitability of the method suggested at the end of this study.