Free Vibration Analysis of Multi-span Timoshenko Beams on Elastic Foundation Using Dynamic Stiffness Method

Abstract

In this study, the exact first five natural frequencies of three-span Timoshenko beams on Winkler foundation are calculated using dynamic stiffness formulation. Different elastic foundation spring constants and different beam cross-sections are used to reflect their effects on natural frequencies. Moreover, the natural frequencies are also calculated via structural analysis software SAP2000 and tabulated with exact results. It is seen that the influence of elastic foundation spring stiffness in inner span is high in comparison with outer spans. The cross-section of the beam plays an important role on natural frequencies of multi-span Timoshenko beams on Winkler foundation.

Keywords

• Dynamic stiffness,free vibration,multi-span Timoshenko beam,Winkler foundation

References

1. [1]. Y. Yesilce, “Determination of Natural Frequencies and Mode Shapes of Axially Moving Timoshenko Beams with Different Boundary Conditions using Differential Transform Method”, Advances in Vibration Engineering, vol. 12, pp. 89-108, 2013.
2. [2]. W. R Chen, “Parametric studies on bending vibration of axially-loaded twisted Timoshenko beams with locally distributed Kelvin–Voigt damping”, International Journal of Mechanical Sciences, vol. 88, pp. 61-70, 2016.
3. [3]. S. G. Kelly, C. Nicely, “Free vibrations of a Series of Beams Connected by Viscoelastic Layers”, Advances in Acoustics and Vibration, Article ID 976841, 8 pages, 2015.
4. [4]. G. Tan, W. Wang , Y. Jiao, “Flexural Free Vibrations of Multistep Nonuniform Beams”, Advances in Acoustics and Vibration, Article ID 7314280, 12 pages, 2016.
5. [5]. B. R. Goncalves, A. Karttunen, J. Romanoff, J. N. Reddy, “Buckling and free vibration of shear-flexible sandwich beams using a couple-stress-based finite element”, Composite Structures, vol. 165, pp. 233-241, 2017.
6. [6]. T. M. Wang, J. E. Stephens, “Natural frequencies of Timoshenko beams on Pasternak foundations”, Journal of Sound and Vibration, Vol. 51(2), pp. 149-155, 1977.
7. [7]. S. Y. Lee, Y. H. Kou, F. Y. Lin, “Stability of a Timoshenko beam resting on a Winkler elastic foundation”, Journal of Sound and Vibration, vol. 153(2), pp. 193-202, 1992.
8. [8]. M. A. De Rosa, “Free vibrations of Timoshenko beams on two-parameter elastic foundation”. Computers & Structures, vol. 57(1), pp. 151-156, 1995.

9. [9]. A. S. Kanani, H. Niknam, A. R. Ohadi, M. M. Aghdam, “Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam”, Composite Structures, vol. 115, pp. 60-68, 2014.
10. [10]. M. Aslami, P. A. Akimov, “Analytical solution for beams with multipoint boundary conditions on two-parameter elastic foundations”, Archives of Civil and Mechanical Engineering, vol. 16(4), pp. 668-677, 2016.
11. [11]. J. R. Banerjee, “Dynamic Stiffness Formulation for Structural Elements: A General Approach”, Computers&Structures, vol. 63, pp. 101-103, 1997.
12. [12]. L. Jun, H. Hongxing, H. Rongying, “Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams”, Computers and Structures, vol. 84, pp. 87-98, 2008.
13. [13]. L. Bao-hui, G. Hang-shan, Z. Hong-bo, L. Yong-shou, Y. Zhou-feng, “Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method”, Nuclear Engineering and Design, vol. 241, pp. 666-671, 2011.
14. [14]. J. R. Banerjee, “Free vibration of beams carrying spring-mass systems - A dynamic stiffness approach”, Computers and Structures, vol. 104-105, pp. 21-26, 2012.
15. [15]. J. R. Banerjee, D. R. Jackson, “Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution”, Computers and Structures, vol. 124, pp. 11-20, 2013.
16. [16]. H. Su, J. R. Banerjee, “Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams”, Computers and Structures, vol. 147, pp. 107-116, 2015.
17. [17]. B. Bozyigit, Y. Yesilce, “Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam”, Structural Engineering and Mechanics, vol. 58(5), pp. 847-868, 2016