How to cite this paper
Lee, B., Oh, S., Lee, T & Kim, G. (2021). Free vibrations of tapered shear deformable column.Engineering Solid Mechanics, 9(1), 1-12.
Refrences
Andrade, A., Camotim, D., & Dinis, P. B. (2007). Lateral-torsional buckling of singly symmetric web-tapered thin-walled I-beams: 1D model vs. shell FEA. Computers & Structures, 85(17-18), 1343-1359.
Burden, R. L., Faires, D. J. & Burden, A. M. (2016). Numerical Analysis. Cengage Learning, MA, USA.
Carpinteri, A., Malvano, R., Manuello, A., & Piana, G. (2014). Fundamental frequency evolution in slender beams subjected to imposed axial displacements. Journal of Sound and Vibration, 333(11), 2390-2403.
Gere, J. M. &Timoshenko, S. P. (1997). Mechanics of Materials. PWS Publishing Company, MA, USA.
Humar, J. L. (2002). Dynamics of Structures. A. A. Balkema Publisher, Rotterdam, Netherlands.
Karnovsky, I. A. & Lebed, O. I. (2000). Formulas for Structural Dynamics. McGraw Hill, NY, USA.
Lee, B. K., Oh, S. J., & Lee, T. E. (2013). Free vibration of tapered Timoshenko beams by deformation decomposition. International Journal of Structural Stability and Dynamics, 13(02), 1250057.
Lee, B. K., Lee, T. E., Choi, J. M., & Oh, S. J. (2012). Dynamic optimal arches with constant volume. International Journal of Structural Stability and Dynamics, 12(06), 1250044.
Lee, J. K. & Lee, B. K. (2020). Buckling optimization of axially functionally graded columns with constant volume. Engineering Optimization (under review).
Li, G. Q. & Li, J. J. (2002). A tapered Timoshenko-Euler beam element for analysis steel portal frame. Journal of Computational Steel Research, 58, 1531-1544.
Loya, J. A., Rubio, L., & Fernández-Sáez, J. (2006). Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290(3-5), 640-653.
Maalek, S. (1999). Shear defection of Tapered Timoshenko beams. International Journal of Mechanical Science, 46, 783-805.
Shimpi, R. P., Shetty, R A. & Guha, A. (2017). A simple single variable shear deformation theory for a rectangular beam. Journal of Mechanical Engineering Science, 231(24), 4576-4591.
Takahashi, I. (1999). Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force. Computational Structure, 71, 585-591.
Timoshenko, S. P. & Young, D. H. (1974). Vibration Problems in Engineering. John Wiley and Sons, NJ, USA.
Viola, E., Ricci, P., & Aliabadi, M. H. (2007). Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method. Journal of Sound and Vibration, 304(1-2), 124-153.
Yang, Y. B., & Yau, J. D. (1987). Stability of beams with tapered I-sections. Journal of Engineering Mechanics, 113(9), 1337-1357.
Yardimoglu, B., & Yildirim, T. (2004). Finite element model for vibration analysis of pre-twisted Timoshenko beam. Journal of Sound and Vibration, 273(4-5), 741-754.
Yau, J. D. (2006). Stability of tapered I-beams under torsional moments. Finite Elements in Analysis and Design, 42(10), 914-927.
Zhou, D. (2001). Free vibration of multi-span Timoshenko beams using static Timoshenko beam functions. Journal of Sound and Vibration, 241(4), 725-734.
Burden, R. L., Faires, D. J. & Burden, A. M. (2016). Numerical Analysis. Cengage Learning, MA, USA.
Carpinteri, A., Malvano, R., Manuello, A., & Piana, G. (2014). Fundamental frequency evolution in slender beams subjected to imposed axial displacements. Journal of Sound and Vibration, 333(11), 2390-2403.
Gere, J. M. &Timoshenko, S. P. (1997). Mechanics of Materials. PWS Publishing Company, MA, USA.
Humar, J. L. (2002). Dynamics of Structures. A. A. Balkema Publisher, Rotterdam, Netherlands.
Karnovsky, I. A. & Lebed, O. I. (2000). Formulas for Structural Dynamics. McGraw Hill, NY, USA.
Lee, B. K., Oh, S. J., & Lee, T. E. (2013). Free vibration of tapered Timoshenko beams by deformation decomposition. International Journal of Structural Stability and Dynamics, 13(02), 1250057.
Lee, B. K., Lee, T. E., Choi, J. M., & Oh, S. J. (2012). Dynamic optimal arches with constant volume. International Journal of Structural Stability and Dynamics, 12(06), 1250044.
Lee, J. K. & Lee, B. K. (2020). Buckling optimization of axially functionally graded columns with constant volume. Engineering Optimization (under review).
Li, G. Q. & Li, J. J. (2002). A tapered Timoshenko-Euler beam element for analysis steel portal frame. Journal of Computational Steel Research, 58, 1531-1544.
Loya, J. A., Rubio, L., & Fernández-Sáez, J. (2006). Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290(3-5), 640-653.
Maalek, S. (1999). Shear defection of Tapered Timoshenko beams. International Journal of Mechanical Science, 46, 783-805.
Shimpi, R. P., Shetty, R A. & Guha, A. (2017). A simple single variable shear deformation theory for a rectangular beam. Journal of Mechanical Engineering Science, 231(24), 4576-4591.
Takahashi, I. (1999). Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force. Computational Structure, 71, 585-591.
Timoshenko, S. P. & Young, D. H. (1974). Vibration Problems in Engineering. John Wiley and Sons, NJ, USA.
Viola, E., Ricci, P., & Aliabadi, M. H. (2007). Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method. Journal of Sound and Vibration, 304(1-2), 124-153.
Yang, Y. B., & Yau, J. D. (1987). Stability of beams with tapered I-sections. Journal of Engineering Mechanics, 113(9), 1337-1357.
Yardimoglu, B., & Yildirim, T. (2004). Finite element model for vibration analysis of pre-twisted Timoshenko beam. Journal of Sound and Vibration, 273(4-5), 741-754.
Yau, J. D. (2006). Stability of tapered I-beams under torsional moments. Finite Elements in Analysis and Design, 42(10), 914-927.
Zhou, D. (2001). Free vibration of multi-span Timoshenko beams using static Timoshenko beam functions. Journal of Sound and Vibration, 241(4), 725-734.