• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.46-49
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• 2008

This paper deals with the free vibrations of elastica shaped arches with constant arc length. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, in-plane vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged end constraints. The effects of rotatory inertia, rise to span length ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica and parabolic shaped arches are compared. Also, typical mode shapes are presented in figures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6A
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• pp.827-833
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• 2008

This paper deals with the free vibrations of elastica shaped arches. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, planar vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effects of rotatory inertia, rise ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica shaped arches are greater than those of parabolic shaped ones. Also, typical mode shapes are presented in figures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.6A
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• pp.617-624
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• 2009

This study deals with the free vibrations of the elastica shaped arch with linear taper. The shape of elastica is obtained from the Bernoulli-Euler beam theory. Differential equations governing free vibrations of such arch are derived and numerically solved to determine natural frequencies, in which three kinds of taper type and two kinds of end constraint, respectively, are considered. For validating the theories presented herein, the frequency parameters obtained in this study are compared to those of SAP 2000. As results of the numerical analyses, effects of end constraint, taper type, slenderness ratio and section ratio on the lowest four non-dimensional frequency parameters are extensively investigated.