17. Linear free vibration analysis of tapered Timoshenko beams using coupled displacement field method
Rajesh Korabathina1, Meera Saheb Koppanati2
Jawaharlal Nehru Technological University, Kakinada, 533003, India
E-mail: firstname.lastname@example.org, email@example.com
(Received 9 November 2015; accepted 19 January 2016)
Abstract. Every structure which is having some mass and elasticity is said to vibrate. Natural frequency is the one of the most important parameter associated with engineering vibration. In nature every structure has its own natural frequency. Whenever the natural frequency of the structure coincides with the frequency of external applied load, excessive deflections will occur and the structure will be failed. To avoid such condition one must be aware of the operating frequencies of the materials or structures under various conditions like simply supported, clamped and cantilever boundary conditions. There are many methods to evaluate the natural frequency of the structures. in this method the authors developed a method called “coupled displacement field method” which reduces computational efforts compared with the other methods and which is successfully applied for the Hinged-Hinged boundary condition of a tapered (rectangular cross section) Timoshenko beam and calculated the fundamental frequency parameter values and compared the results with existing literature. The results obtained in this method are very close to the existing literature.
Keywords: linear free vibrations, coupled displacement filed method, tapered Timoshenko beams, taper ratio, slenderness ratio.
 Abrate S. Vibration of non-uniform rods and beams. Journal of Sound and Vibration, Vol. 185, Issue 4, 1995, p. 703‑716.
 Byoung Koo Lee, et al. Free vibrations of tapered Beams with general boundary condition. Journal of Civil Engineering, Vol. 6, Issue 3, 2002, p. 283‑288.
 De Rosa M. A., Auciello N. M. Free vibrations of tapered beams with flexible ends. Journal of Computers and Structures, Vol. 60, Issue 2, 1996, p. 197‑202.
 De Rosa M. A., Lippiello M. Natural vibration frequencies of tapered beams. Journal of Engineering Transactions, Vol. 57, Issue 1, 2009, p. 45‑66.
 Firouz-Abadi R. D, et al. An asymptotic solution to transverse free vibrations of variable‑section beams. Journal of Sound and Vibration, Vol. 304, 2007, p. 530‑540.
 Izabela Zamorska Free Transverse vibrations of non-uniform beams. Scientific Research of the Institute of Mathematics and Computer Science, Vol. 9, Issue 2, 2010, p. 244‑250.
 Mahmoud A. A., et al. Free vibrations of uniform and non-uniform Euler beam using differential transformation method. Asian Journal of Mathematics and Applications, Vol. 2013, 2013, p. 1‑16.
 Mehmet Cem Ece, et al. Vibration of a variable cross-section beam. Journal of Mechanics Research Communications, Vol. 34, 2007, p. 78‑84.
 Mohamed Hussien Taha, Samir Abohadima Mathematical model for vibrations of non-uniform flexural beams. Journal of Engineering Mechanics, Vol. 15, Issue 1, 2008, p. 3‑11.
 Rossi R. E., Laura P. A. A. Numerical experiments on vibrating, linearly tapered Timoshenko beams. Journal of Sound and Vibration, Vol. 168, Issue 1, 1993, p. 179‑183.
 Stanisùaw Kukla, Izabela Zamojska Application of the Green’s function method in free vibration analysis of non-uniform beams. Scientific Research of the Institute of Mathematics and Computer Science, Vol. 4, Issue 1, 2005, p. 87‑94.
 Zhou D., Cheung Y. K. The free vibration of a type of tapered beams. Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 188, 2000, p. 203‑216.
Cite this article
Korabathina Rajesh, Koppanati Meera Saheb Linear free vibration analysis of tapered Timoshenko beams using coupled displacement field method. Mathematical Models in Engineering, Vol. 2, Issue 1, 2016, p. 27‑33.
Mathematical Models in Engineering. June 2016, Volume 2, Issue 1
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