• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.942-947
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• 2004

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.131-152
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• 2012

In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant cross-sections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.768-771
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• 2005

The purpose of this paper is to investigate the free vibration of stepped noncircular arches. Taking into account the effects of axial deformation, rotatory inertia and shear deformation, the governing differential equations are solved numerically for the elliptic and sinusoidal geometries with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. The lowest four natural frequencies are presented as functions of four non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, the section ratio, and the discontinuous sector ratio.