• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1181-1184
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• 2007

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with rotationally flexible supports, including the effects of rotatory inertia, shear deformation and axial deformation, are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and the corresponding mode shapes are obtained over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, and the rotational spring stiffness.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.144-152
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• 2010

This paper deals with free vibrations of the tapered circular arches with constant volume, whose cross sectional shape is the solid regular polygon. Volumes of the objective arches are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such arches 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 arch parameters such as rise ratio, section ratio, side number, volume ratio and taper type are reported in tables and figures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1043-1052
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• 2014

This paper deals with in-plane free vibrations of the horseshoe circular arch. Simultaneous ordinary differential equations governing free vibration of the arch are derived with respect to the radial and tangential deformations. Particularly, differential equations are obtained under the arc length coordinate rather than the angular one in order to extend the horseshoe arch whose subtended angle is greater than ${\pi}$ radians. The differential equations are numerically solved for calculating the natural frequencies accompanying with the corresponding mode shapes. In parametric studies, effects of the rotatory inertia, slenderness ratio and circumferential arc length ratio on frequency parameters are extensively discussed.

• Computational Structural Engineering
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• v.7 no.1
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• pp.69-81
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• 1994

This paper summarizes a dynamic analysis of the shallow circular arches under dynamic loading, considering the geometric nonlinearity. The major emphasis is placed on the development of computer program, which is utilized for the analysis of the nonlinear dynamic behavior and for the evaluation of the critical buckling loads of the shallow circular arches. Geometric nonlinearity is modeled using Lagrangian description of the motion and a finite element analysis procedure is used to solve the dynamic equation of motion. A circular arch subject to normal step load is analyzed and the results are compared with those from other researches to verify the developed program. The critical buckling loads of arches are estimated using the non-dimensional time, load and shape parameters and the results are also compared with those from the linear analysis. It is found that geometric nonlinearity plays and important role in the analysis of shallow arches and the probability of buckling failure is getting higher as arches become shallower.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.2
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• pp.39-48
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• 1990

For shallow circular arches with large dynamic loading, use of linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of the shallow circular arches in which geometric nonlinearity is dominant. A program is developed for analysis of the nonlinear dynamic behavior and for evaluation of the critical buckling loads of the shallow circular arches. Geometric nonlinearity is modeled using Lagrangian description of the motion and finite element analysis procedure is used to solve the dynamic equations of motion in which Newmark method is adopted as a time marching scheme. A shallow circular arch subject to radial step load is analyzed and the results are compared with those from other researches to verify the developed program. The critical buckling loads of shallow arches are evaluated using the non-dimensional parameter. Also, the results are compared with those from linear analysis.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.43-54
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• 1992

For shallow arches with large dynamic loading, linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of shallow arches in which geometric nonlinearity must be considered. A program is developed for the analysis of the nonlinear dynamic behavior and for evaluation of critical buckling loads of shallow arches. Geometric nonlinearity is modeled using Lagrangian description of the motion. The finite element analysis procedure is used to solve the dynamic equation of motion and Newmark method is adopted in the approximation of time integration. A shallow arch subject to radial step loads is analyzed. The results are compared with those from other researches to verify the developed program. The behavior of arches is analyzed using the non-dimensional time, load, and shape parameters. It is shown that geometric nonlinearity should be considered in the analysis of shallow arches and probability of buckling failure is getting higher as arches are getting shallower. It is confirmed that arches with the same shape parameter have the same deflection ratio at the same time parameter when arches are loaded with the same parametric load. In addition, it is proved that buckling of arches with the same shape parameter occurs at the same load parameter. Circular arches, which are under a single or uniform normal load, are analyzed for comparison. A parabolic arch with radial step load is also analyzed. It is verified that the developed program is applicable for those problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.357-364
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• 2008

This paper deals with the free vibrations of arches with rectangular hollow section having constant area. The differential equations governing free vibrations of arches are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with clamped-clamped, clamped-hinged and hinged-hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the shape ratio

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.81-89
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• 2004

The vibration analysis of the circular arch as a member of a structure has been an important subject of mechanics due to its various applications to many industrial fields. In particular, circular arches with variable cross section are widely used to optimize the distribution of weight and strength and to satisfy special architectural and functional requirements. The Generalized Differential Quadrature Method (GDQM) and Differential Transformation Method (DTM) were recently proposed by Shu and Zou, respectively. In this study, GDQM and DTM were applied to the vibration analysis of circular arches with variable cross section. The governing equations of motion for circular arches with variable cross section were derived. The concepts of Differential Transformation and Generalized Differential Quadrature were briefly introduced. The non-dimensionless natural frequencies of circular arches with variable cross section were obtained for various boundary conditions. The results obtained using these methods were compared with those of previous works. GDQM and DTM showed fast convergence, accuracy, efficiency, and validity in solving the vibration problem of circular arches with variable cross section.

• Journal of architectural history
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• v.7 no.4 s.17
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• pp.191-198
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• 1998

The form of Pantheon in Rome is graphically analyzed in relation to the angle of the Sun that varies through four seasons of the year. These are worked out in the Autocad drawing files for exactitude and efficiency. Some of the results suggest that the Pantheon is carefully designed to predict the equinoxes and the solstices.