Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Accurate periodic solution for nonlinear vibration of thick circular sector slab

  • Pakar, Iman (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahmoud (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahdi (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University)
  • Received : 2014.01.12
  • Accepted : 2014.02.25
  • Published : 2014.05.25
⟨ Previous Next ⟩

Abstract

In this paper we consider a periodic solution for nonlinear free vibration of conservative systems for thick circular sector slabs. In Energy Balance Method (EBM) contrary to the conventional methods, only one iteration leads to high accuracy of the solutions. The excellent agreement of the approximate frequencies and periodic solutions with the exact ones could be established. Some patterns are given to illustrate the effectiveness and convenience of the methodology. Comparing with numerical solutions shows that the energy balance method can converge to the numerical solutions very rapidly which are valid for a wide range of vibration amplitudes as indicated in this paper.

Keywords

References

  1. Cordero, A., Hueso, J.L., Martinez, E. and Torregros, J.R. (2010), "Iterative methods for use with nonlinear discrete algebraic models", Math. Comput. Model., 52(7-8), 1251-1257. https://doi.org/10.1016/j.mcm.2010.02.028
  2. Bayat, M. and Pakar, I, (2011a), "Nonlinear free vibration analysis of tapered beams by Hamiltonian Approach", J. Vibroeng., 13(4), 654-661.
  3. Bayat, M. and Pakar, I. (2011b), "Application of He's energy balance method for nonlinear vibration of thin circular sector cylinder", Int. J. Phy. Sci., 6(23), 5564-5570.
  4. Bayat, M. and Pakar, I. (2012), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., Int. J., 43(3), 337-347. https://doi.org/10.12989/sem.2012.43.3.337
  5. Bayat, M. and Pakar, I. (2013a), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420 . https://doi.org/10.1007/s11803-013-0182-0
  6. Bayat, M. and Pakar, I. (2013b), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52. https://doi.org/10.1155/2013/549213
  7. Bayat, M., Pakar, I. and Shahidi, M. (2011), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.
  8. Bayat, M., Pakar, I. and Domaiirry, G. (2012), "Recent developments of Some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review", Latin American J. Solid. Struct., 9(2), 145-234.
  9. Bayat, M., Pakar, I. and Bayat, M. (2013), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., Int. J., 14(5), 511-521. https://doi.org/10.12989/scs.2013.14.5.511
  10. Bayat, M., Pakar, I. and Cveticanin, L. (2014a), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: an analytical approach", Mech. Machine Theory, 77, 50-58. DOI: 10.1016/j.mechmachtheory.2014.02.009
  11. Bayat, M., Pakar, I. and Cveticanin, L. (2014b), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Archive Appl. Mech., 84(1), 43-50. https://doi.org/10.1007/s00419-013-0781-2
  12. Bayat, M., Bayat, M. and Pakar, I. (2014c), "Nonlinear vibration of an electrostatically actuated microbeam", Latin Am. J. Solid. Struct., 11(3), 534-544. https://doi.org/10.1590/S1679-78252014000300009
  13. Kuo, B.L. and Lo, C.Y. (2009), "Application of the differential transformation method to the solution of a damped system with high nonlinearity", Nonlinear Anal., 70(4), 1732-1737. https://doi.org/10.1016/j.na.2008.02.056
  14. Dehghan, M. and Tatari, M. (2008), "Identifying an unknown function in a parabolic equation with over specified data via He's variational iteration method", Chaos Soliton. Fract., 36(1), 157-166. https://doi.org/10.1016/j.chaos.2006.06.023
  15. He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillators", Mech. Res. Comm., 29(2), 107-111. https://doi.org/10.1016/S0093-6413(02)00237-9
  16. He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Soliton. Fract., 34(5), 1430-1439. https://doi.org/10.1016/j.chaos.2006.10.026
  17. He J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlinear Sci. Numer. Simul., 9(2), 211-212.
  18. Mehdipour, I., Ganji, D.D. and Mozaffari, M. (2010), "Application of the energy balance method to nonlinear vibrating equations", Current Appl. Phys., 10(1), 104-112. https://doi.org/10.1016/j.cap.2009.05.016
  19. Odibat, Z., Momani, S, and Suat Erturk, V. (2008), "Generalized differential transform method: application to differential equations of fractional order", Appl. Math. Comput., 197(2) , 467-477. https://doi.org/10.1016/j.amc.2007.07.068
  20. Pakar, I. and Bayat, M. (2011), "Analytical solution for strongly nonlinear oscillation systems using energy balance method", Int. J. Phys. Sci., 6(22), 5166-5170.
  21. Pakar, I. and Bayat, M. (2012), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.
  22. Pakar, I. and Bayat, M. (2013a), "An analytical study of nonlinear vibrations of buckled Euler_Bernoulli beams", Acta Physica Polonica A, 123(1), 48-52. https://doi.org/10.12693/APhysPolA.123.48
  23. Pakar, I. and Bayat, M. (2013b), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., Int. J., 46(1), 137-151. https://doi.org/10.12989/sem.2013.46.1.137
  24. Pakar, I., Bayat, M. and Bayat, M. (2012), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.
  25. Shaban, M., Ganji, D.D. and Alipour, A.A. (2010), "Nonlinear fluctuation, frequency and stability analyses in free vibration of circular sector oscillation systems", Current Appl. Phys., 10(5), 1267-1285. https://doi.org/10.1016/j.cap.2010.03.005
  26. Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133. https://doi.org/10.1016/j.camwa.2009.03.056
  27. Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108. https://doi.org/10.1016/j.mcm.2011.05.018
  28. Xu, L. (2008), "Variational approach to solution of nonlinear dispersive K(m, n) equation", Chaos Soliton. Fract., 37(1), 137-143. https://doi.org/10.1016/j.chaos.2006.08.016
  29. Xu, L. and Zhang, N. (2009), "Variational approachnext term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463. https://doi.org/10.1016/j.camwa.2009.03.035
  30. Zeng, D.Q. and Lee, Y.Y. (2009), "Analysis of strongly nonlinear oscillator using the max-min approach", Int. J. Nonlinear Sci. Numer. Simul., 10(10), 1361-1368.

Cited by

  1. Effect of granulated rubber on shear strength of fine-grained sand vol.9, pp.5, 2017, https://doi.org/10.1016/j.jrmge.2017.03.008
  2. Analytical study of nonlinear vibration of oscillators with damping vol.9, pp.1, 2015, https://doi.org/10.12989/eas.2015.9.1.221
  3. High conservative nonlinear vibration equations by means of energy balance method vol.11, pp.1, 2016, https://doi.org/10.12989/eas.2016.11.1.129
  4. Study of complex nonlinear vibrations by means of accurate analytical approach vol.17, pp.5, 2014, https://doi.org/10.12989/scs.2014.17.5.721
  5. A novel approximate solution for nonlinear problems of vibratory systems vol.57, pp.6, 2016, https://doi.org/10.12989/sem.2016.57.6.1039
  6. Accurate analytical solutions for nonlinear oscillators with discontinuous vol.51, pp.2, 2014, https://doi.org/10.12989/sem.2014.51.2.349
  7. Prediction of Liquefaction Potential of Sandy Soil around a Submarine Pipeline under Earthquake Loading vol.10, pp.2, 2019, https://doi.org/10.1061/(ASCE)PS.1949-1204.0000349
  8. Shear behavior of fiber-reinforced sand composite vol.12, pp.5, 2019, https://doi.org/10.1007/s12517-019-4326-z
  9. Experimental study of impact of cement treatment on the shear behavior of loess and clay vol.13, pp.4, 2014, https://doi.org/10.1007/s12517-020-5181-7
  10. Comparison of different local site effect estimation methods in site with high thickness of alluvial layer deposits: a case study of Babol city vol.13, pp.7, 2014, https://doi.org/10.1007/s12517-020-5258-3