- Volume 52 Issue 5
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Vibrations of rotationally restrained Timoshenko beam at hinged supports during an earthquake
- Kim, Yong-Woo (Department of Mechanical Engineering, Sunchon National University) ;
- Ryu, Jeong Yeon (Department of Mechanical Engineering, Graduate School of Sunchon National University)
- Received : 2019.05.07
- Accepted : 2019.10.29
- Published : 2020.05.25
The present paper describes an analytic solution procedure for flexural vibration of a rotationally restrained hinged-hinged Timoshenko beam at the supports during an earthquake. Focusing on maximal magnitudes of internal loads such as bending moment and shearing force under wide variations of two parameters, kL/EI and kGAL2/EI, various beams under synchronous and asynchronous support motions are simulated. The simulations under asynchronous support motions show the following facts. The variations of the maximal magnitudes of internal loads of stocky beams due to the variation of kL/EI from zero to infinity show much wider variations than those of slender beams as kGAL2/EI decreases. The maximal magnitudes of internal loads of a beam tend to be governed by their static components as kL/EI increases and kGAL2/EI decreases. When the internal loads are governed by their static components, maximal magnitudes of internal loads of the stocky tend to increase monotonically as the value of kL/EI increases. However, the simulations under synchronous support motions show the static components of the internal loads vanish and the internal loads are governed by dynamic components irrespective of the two parameters.
- B.A.H. Abbas, Vibrations of Timoshenko beams with elastically restrained ends, J. Sound Vib. 97 (4) (1984) 541-548.
- P.A.A. Laura, P.M. Belles, R.E. Rossi, M.J. Maurizi, Natural frequencies of Timoshenko beams elastically restrained against translation and rotation at one end, J. Acoust. Soc. Am. 90 (1991) 2199-2201.
- S.H. Farghaly, Vibration and stability analysis of Timoshenko beams with discontinuities in cross-section, J. Sound Vib. 174 (5) (1994) 591-605.
- S.Y. Lee, S.M. Lin, Vibrations of elastically restrained non-uniform Timoshenko beams, J. Eng. Nat. Sci. 183 (3) (1995) 403-415.
- T. Kocaturk, M. Simsek, Free vibration analysis of elastically supported Timoshenko beams, J. Eng. Nat. Sci. 3 (2005) 79-93.
- O. Demirgag, Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods, Sadhana 33 (1) (2008) 57-68.
- V. Quintana, J. Raffo, R.O. Grossi, Eigenfrequencies of generally restrained Timoshenko beams with an internal hinge, Mechanica Comput. 29 (2010) 2499-2516.
- D. Shi, Q. Wang, X. Shi, F. Pang, An accurate solution method for the vibration analysis of Timoshenko beams with general elastic supports, Proc IMecE Part C: J. Mech. Eng. Sci. 229 (13) (2015) 2327-2340.
- A. Soares, A.C. Azevedo, S.S. Hoefel, Dynamic analysis of elastically supported Timoshenko beam, in: CILAMCE 2016, Proceedings of the XXXVII Iberian Latin_American Congress on Computational Methods in Engineering, 2016.
- S.Y. Lee, S.M. Lin, Non-uniform Timoshenko beams with time-dependent elastic boundary conditions, J. Sound Vib. 217 (9) (1998) 223-238.
- S.M. Lin, S.Y. Lee, The forced vibration and boundary control of pretwisted Timoshenko beams with general time dependent elastic boundary conditions, J. Sound Vib. 254 (1) (2002) 69-90.
- Y.-W. Kim, Dynamic analysis of Timoshenko beam subjected to support motions, J. Mech. Sci. Technol. 30 (2) (2016) 4167-4176.
- Y.-W. Kim, Analytic solution of Timoshenko beam excited by real seismic support motions, Struct. Eng. Mech. 62 (2) (2017) 247-258.
- S.M. Han, H. Benaroya, T. Wei, Dynamics of transversely vibrating beams using four engineering theories, J. Sound Vib. 225 (3) (1999) 935-988.
- N.F.J. van Rensburg, A.J. van der Merwe, Natural frequencies and modes of a Timoshenko beam, Wave Motion 44 (2006) 58-69.
- L. Majkut, Free and forced vibrations of Timoshenko beams described by single difference equation, J. Theor. Appl. Mech. 47 (1) (2009) 193-210.
- J.R. Hutchinson, Shear coefficients for Timoshenko beam theory, J. Appl. Mech. 68 (2001) 87-92.