Out-of-Plane Vibration Analysis of Multiple-Stepped Circular Beam

Abstract

Stepped circular beams are widely used in various engineering fields. Thus, studying the free vibration characteristics of those structures is an essential subject of research. The unified approach of the Complementary Functions Method (CFM) and the Laplace transform is employed in this paper to examine the out-of-plane free vibration analyses of the circular Timoshenko beams with multiple stepped cross-section. The proposed procedure can be used to investigate the natural frequencies of circular rods consisting of an arbitrary number of steps through the curvature. The material of the beam considered to be isotropic, homogeneous and elastic. By considering the effects of shear deformation and rotary inertia, the equations of motion of the circular beam are introduced. Obtained equations are transformed to the Laplace domain and solved numerically by the CFM. Comparisons of the results with those of ANSYS show that the suggested scheme is applicable and of high precision for out-of-plane free vibration analysis of multi-stepped circular beams.

Keywords

• Out-of-plane free vibration,Multi-stepped circular beam,Laplace transform

References

1. Kawakami M, Sakiyama T, Matsuda H, Morita C, (1995). In-Plane and out-of-plane free vibrations of curved beams with variable cross-sections. Journal of Sound and Vibration 187: 381-401.
2. Howson W P, Jemah A K, (1999). Exact out-of-plane natural frequencies of curved Timoshenko beams. Journal of Engineering Mechanics 125: 19-25.
3. Wu J S, Chiang L K, (2004). A new approach for free vibration analysis of arches with effects of shear deformation and rotary inertia considered. Journal of Sound and Vibration 277: 49-71.
4. Wu J S, Chen Y C, (2011). Out-of-plane free vibration analysis of a horizontally circular curved beam carrying arbitrary sets of concentrated elements. Journal of Structural Engineering, 10.1061, ASCE_ST.1943- 541X.0000290.
5. Doğruer O Y, (2006). Analytical solutions of out- of-plane static and dynamic problems of planar curved beams, Istanbul Technical University, Istanbul, PhD. Thesis.
6. Tüfekci E, Doğruer O Y, (2006). Out of plane free vibration of a circular arch with uniform cross-section: Exact solution, J. Sound Vib. 291: 525-538.
7. Eroğlu U, (2014). Finite element analysis of curved beams using exact solutions, Istanbul Technical University, Istanbul, MSc. Thesis.
8. Manolis G D, Beskos D E, (1982). Dynamic response of framed underground structures, Comp. and Struct. 15(5): 521-531.

9. Beskos D E, Narayanan G V, (1983). Dynamic response of frameworks by numerical Laplace transform. Computer Methods in Applied Mechanical and Engineering, 37(3): 289-307.
10. Aslan T A, Noori A R, Temel B, (2017). Forced vibration of out of plane loaded stepped circular rods. International Conference on Civil and Environmental Engineering, May 8-10, Nevsehir, Turkey, 2062- 2074.
11. Noori A R, Aslan T A, Temel B, (2018). Damped transient response of in-plane and out-of-plane loaded stepped curved rods. Journal of the Brazilian Society of Mechanical Sciences and Engineering 40: 1-24.
12. Yarımpabuç D, Eker M, Çelebi K, (2018). Mechanical behavior of functionally graded pressure vessels under the effect of Moisson’s ratio. European Mechanical Science 2(2): 52-59.
13. ANSYS Swanson Analysis System, Inc., 201 Johnson Road, Houston, PA15342-1300,USA.