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Structural Engineering and Mechanics Volume 42, Number 2, April25 2012 , pages 131-152 DOI: https://doi.org/10.12989/sem.2012.42.2.131 |
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Effects of geometric parameters on in-plane vibrations of two-stepped circular beams |
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Ekrem Tufekci and Oznur Ozdemirci Yigit
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| Abstract | ||
| 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 crosssections. 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. | ||
| Key Words | ||
| curved beam; stepped arch; free vibration; in-plane; exact solution; mode transition | ||
| Address | ||
| Ekrem Tufekci and Oznur Ozdemirci Yigit: Faculty of Mechanical Engineering, Istanbul Technical University, Gumussuyu, TR34437 Istanbul, Turkey | ||