An Analytical Study of Nonlinear Vibrations οf Buckled Euler-Bernoulli Beams

• Authors: I. Pakar , M. Bayat
• Languages of publication: EN

Abstracts

EN

The current research deals with a way of using a new kind of periodic solutions called He's max-min approach for the nonlinear vibration of axially loaded Euler-Bernoulli beams. By applying this technique, the beam's natural frequencies and mode shapes can be easily obtained and a rapidly convergent sequence is obtained during the solution. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. To verify the results some comparisons are presented between max-min approach results and the exact ones to show the accuracy of this new approach. It has been discovered that the max-min approach does not necessitate small perturbation and is also suitably precise to both linear and nonlinear problems in physics and engineering.

Keywords

EN

42.65.Wi; 46.70.De; 44.05.+e

Discipline

• 42.65.Wi: Nonlinear waveguides
• 46.70.De: Beams, plates, and shells
• 44.05.+e: Analytical and numerical techniques

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 123
• Issue: 1
• Pages: 48-52

Dates

published

2013-01

received

2012-05-28

(unknown)

2012-10-25

Contributors

author

I. Pakar

• Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

author

M. Bayat

• Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

References

• [1] D. Burgreen, J. Appl. Mech. 18, 135 (1951)
• [2] F.C. Moon, J. Appl. Mech. 47, 638 (1980)
• [3] P.J. Holmes, F.C. Moon, J. Appl. Mech. 50, 1021 (1983)
• [4] A.M. Abou-Rayan, A.H. Nayfeh, D.T. Mook, Nonlin. Dyn. 4, 499 (1993)
• [5] S.A. Ramu, T.S. Sankar, R. Ganesan, Int. J. Non-Lin. Mech. 29, 449 (1994)
• [6] T.S. Reynolds, E.H. Dowell, Int. J. Non-Lin. Mech. 31, 931 (1996)
• [7] T.S. Reynolds, E.H. Dowell, Int. J. Non-Lin. Mech. 31, 941 (1996)
• [8] W. Lestari, S. Hanagud, Int. J. Non-Lin. Mech. 38, 4741 (2001)
• [9] W.H. Liu, H.S. Kuo, F.S. Yang, J. Sound Vibrat. 121, 375 (1988)
• [10] E. Sevin, J. Sound Vibrat. 27, 125 (1960)
• [11] M. Bayat, I. Pakar, M. Bayat, Latin Am. J. Solids Struct. 8, 149 (2011)
• [12] M. Bayat, I. Pakar, M. Bayat, Int. J. Phys. Sci. 7, 913 (2012)
• [13] M. Bayat, M. Shahidi, A. Barari, G. Domairry, Zeitschr. Naturforsch. Sect. A-A J. Phys. Sci. 66, 67 (2011)
• [14] I. Pakar, M. Bayat, M. Bayat, Int. J. Phys. Sci. 6, 6861 (2011)
• [15] M. Shahidi, M. Bayat, I. Pakar, G. Abdollahzadeh, Int. J. Phys. Sci. 6, 1628 (2011)
• [16] M. Bayat, I. Pakar, M. Shahidi, Mechanika 17, 620 (2011)
• [17] M. Bayat, M. Shahidi, M. Bayat, Int. J. Phys. Sci. 6, 3608 (2011)
• [18] M. Bayat, I. Pakar, J. Vibroeng. 13, 654 (2011)
• [19] I. Pakar, M. Bayat, M. Bayat, J. Vibroeng. 14, 423 (2012)
• [20] M. Sathyamoorthy, Shock Vib. Dig. 14, 19 (1982)
• [21] M. Bayat, I. Pakar, G. Domaiirry, Latin Am. J. Solids Struct. 9, 145 (2012)
• [22] M. Bayat, I. Pakar, Struct. Eng. Mech. 43, 337 (2012)
• [23] I. Pakar, M. Bayat, J. Vibroeng. 14, 216 (2012)
• [24] M. Bayat, I. Pakar, Shock and Vibration
• [25] E. Ghasemi , M. Bayat, M. Bayat, Int. J. Phys. Sci. 6, 5022 (2011)
• [26] H.Y. Lai, J.C. Hsu, C.K. Chen, Computers Math. Appl. 56, 3204 (2008)
• [27] S. Naguleswaran, Int. J. Mech. Sci. 45, 1563 (2003)
• [28] T. Pirbodaghi, M.T. Ahmadian, M. Fesanghary, Mech. Res. Commun. 36, 143 (2009)
• [29] Y. Liu, S.C. Gurram, Math. Comput. Model. 50, 1545 (2009)
• [30] M. Bayat, A. Barari, M. Shahidi, Mechanika 17, 172 (2011)
• [31] I. Pakar, M. Bayat, J. Vibroeng. 14, 216 (2012)
• [32] S.R.R. Pillai, B.N. Rao, J. Sound Vibrat. 159, 527 (1992)
• [33] J.H. He, Int. J. Nonlin. Sci. Numer. Simul. 9, 207 (2008)
• [34] J.H. He, Appl. Mech. Comput. 151, 887 (2004)
• [35] J.H. He, Appl. Math. Comput. 151, 293 (2004)
• [36] L. Azrar, R. Benamar, R.G.A. White, J. Sound Vibrat. 224, 183 (1999)

Identifiers

DOI

10.12693/APhysPolA.123.48