JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A novel approximate solution for nonlinear problems of vibratory systems
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A novel approximate solution for nonlinear problems of vibratory systems
Edalati, Seyyed A.; Bayat, Mahmoud; Pakar, Iman; Bayat, Mahdi;
 Abstract
In this research, an approximate analytical solution has been presented for nonlinear problems of vibratory systems in mechanical engineering. The new method is called Variational Approach (VA) which is applied in two different high nonlinear cases. It has been shown that the presented approach leads us to an accurate approximate analytical solution. The results of variational approach are compared with numerical solutions. The full procedure of the numerical solution is also presented. The results are shown that the variatioanl approach can be an efficient and practical mathematical tool in field of nonlinear vibration.
 Keywords
variational approach method;nonlinear vibration;numerical method;
 Language
English
 Cited by
1.
Effect of granulated rubber on shear strength of fine-grained sand, Journal of Rock Mechanics and Geotechnical Engineering, 2017, 9, 5, 936  crossref(new windwow)
 References
1.
Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. crossref(new window)

2.
Atmane, H.A., Tounsi, A., Ziane, N. and Mechab, I. (2011), "Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section", Steel Compos. Struct., 11(6), 489-504. crossref(new window)

3.
Bayat, M. and Pakar, I. (2013a), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52. crossref(new window)

4.
Bayat, M. and Pakar, I. (2012a), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., 43(3), 337-347. crossref(new window)

5.
Bayat, M., Pakar, I. and Domaiirry, G. (2012b), "Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review", Latin Am. J. Solid. Struct., 9(2),145-234.

6.
Bayat, M., Pakar, I. and Cveticanin, L. (2014d), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities : an analytical approach", Mech. Mach. Theory., 77, 50-58. crossref(new window)

7.
Bayat, M., Pakar, I. and Cveticanin, L. (2014e), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Arch. Appl. Mech., 84(1), 43-50. crossref(new window)

8.
Bayat, M. and Pakar, I. (2013c), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420. crossref(new window)

9.
Bayat, M., Pakar, I. and Bayat, M. (2013b), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., 14(5), 511-521. crossref(new window)

10.
Bayat, M. and Abdollahzadeh, G. (2011), "On the effect of the near field records on the steel braced frames equipped with energy dissipating devices", Latin Am. J. Solid. Struct., 8(4), 429-443. crossref(new window)

11.
Bayat, M., Bayat, M. and Pakar, I. (2014f), "Nonlinear vibration of an electrostatically actuated microbeam", Latin Am. J. Solid. Struct., 11(3), 534-544. crossref(new window)

12.
Bayat, M., Bayat, M. and Pakar, I. (2014a), "The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading", Steel Compos. Struct., 17(1), 123-131. crossref(new window)

13.
Bayat, M., Bayat, M. and Pakar, I. (2014c), "Forced nonlinear vibration by means of two approximate analytical solutions", Struct. Eng. Mech., 50(6), 853-862 crossref(new window)

14.
Bayat, M., Bayat, M. and Pakar, I. (2014g), "Accurate analytical solutions for nonlinear oscillators with discontinuous", Struct. Eng. Mech., 51(2), 349-360 crossref(new window)

15.
Bayat, M., Pakar, I. and Bayat, M. (2013b), "On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams", Steel Compos. Struct., 14(1), 73-83 crossref(new window)

16.
Bayat, M., Pakar, I. and Bayat, M. (2014b), "An accurate novel method for solving nonlinear mechanical systems", Struct. Eng. Mech., 51(3), 519-530. crossref(new window)

17.
Bayat, M., Pakar, I. and Emadi, A. (2013a), "Vibration of electrostatically actuated microbeam by means of homotopy perturbation method", Struct. Eng. Mech., 48(6), 823-831. crossref(new window)

18.
Bararnia, H., Domairry, G., Gorji, M. and Rezania, A. (2010), "An approximation of the analytic solution of some nonlinear heat transfer in fin and 3D diffusion equations using HAM", Numer. Meth. Part. Differ. Eq., 26(1), 1-13. crossref(new window)

19.
Bor-Lih, K. and Cheng-Ying, L. (2009), "Application of the differential transformation method to the solution of a damped system with high nonlinearity", Nonlin. Anal., 70(4), 1732-1737. crossref(new window)

20.
Cai, X.C. and Liu, J.F. (2011), "Application of the modified frequency formulation to a nonlinear oscillator", Comput. Math. Appl., 61(8), 2237-2240. crossref(new window)

21.
Chen, S.S. (2009), "Application of the differential transformation method to the free vibrations of strongly non-linear oscillators", Nonlin. Anal. Real World Appl., 10(2), 881-888. crossref(new window)

22.
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. crossref(new window)

23.
Cunedioglu, Y. and Beylergil, B. (2014), "Free vibration analysis of laminated composite beam under room and high temperatures", Struct. Eng. Mech., 51(1), 111-130. crossref(new window)

24.
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 Solit. Fract., 36(1), 157-166. crossref(new window)

25.
Filobello-Nino, U., Vazquez-Leal, H., Benhammouda, B., Perez-Sesma, A., Jimenez-Fernandez, V., Cervantes-Perez, J., Sarmiento-Reyes, A., Huerta-Chua, J., Morales-Mendoza, L. and Gonzalez-Lee, M. (2015), "Analytical solutions for systems of singular partial differential-algebraic equations", Discrete Dyn. Nature Soc., Article ID 752523.

26.
Ganji, D., Nourollahi, M. and Rostamian, M. (2007), "A comparison of variational iteration method with Adomian's decomposition method in some highly nonlinear equations", Int. J. Sci. Tech., 2(2), 179-188.

27.
He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Solit. Fract., 34(5), 1430-1439. crossref(new window)

28.
He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314. crossref(new window)

29.
He, J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlin. Sci. Numer. Simul., 9(2), 211-212.

30.
Jamshidi, N. and Ganji, D.D. (2010), "Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire", Curr. Appl. Phys., 10, 484-486. crossref(new window)

31.
Mehdipour, I., Ganji, D.D. and Mozaffari, M. (2010), "Application of the energy balance method to nonlinear vibrating equations", Curr. Appl. Phys., 10(1), 104-112. crossref(new window)

32.
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.

33.
Pakar, I. and Bayat, M. (2013), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., 46(1), 137-151. crossref(new window)

34.
Pakar, I., Bayat, M. and Bayat, M. (2011), "Analytical evaluation of the nonlinear vibration of a solid circular sector object", Int. J. Phys. Sci., 6(30), 6861-6866.

35.
Pakar, I., Bayat, M. and Bayat, M. (2014a), "Nonlinear vibration of thin circular sector cylinder: an analytical approach", Steel Compos. Struct., 17(1), 133-143. crossref(new window)

36.
Pakar, I., Bayat, M. and Bayat, M. (2014b), "Accurate periodic solution for nonlinear vibration of thick circular sector slab", Steel Compos. Struct., 16(5), 521-531 crossref(new window)

37.
Radomirovic, D. and Kovacic, I. (2015), "An equivalent spring for nonlinear springs in series", Eur. J. Phys., 36(5), 055004. crossref(new window)

38.
Rajasekaran, S. (2013), "Free vibration of tapered arches made of axially functionally graded materials", Struct. Eng. Mech., 45(4), 569-594. crossref(new window)

39.
Sadighi, A. and Ganji, D. (2008), "Analytic treatment of linear and nonlinear Schrodinger equations: a study with homotopy-perturbation and Adomian decomposition methods", Phys. Lett. A, 372(4), 465-469. crossref(new window)

40.
Shahidi, M., Bayat, M., Pakar, I. and Abdollahzadeh, G.R. (2011), "Solution of free non-linear vibration of beams", Int. J. Phys. Sci., 6(7), 1628-1634.

41.
Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133. crossref(new window)

42.
Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108. crossref(new window)

43.
Xu, L. (2010), "Application of Hamiltonian approach to an oscillation of a mass attached to a stretched elastic wire", Comput. Math. Appl., 15(5), 901-906.

44.
Xu, N. and Zhang, A. (2009), "Variational approachnext term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463. crossref(new window)

45.
Xu, R., Li, D.X., Jiang, J.P. and Liu, W. (2015), "Nonlinear vibration analysis of membrane SAR antenna structure adopting a vector form intrinsic finite element", J. Mech., 31(3), 269-277. crossref(new window)

46.
Zeng, D.Q. and Lee, Y.Y. (2009), "Analysis of strongly nonlinear oscillator using the max-min approach", Int. J. Nonlin. Sci. Numer. Simul., 10(10), 1361-1368.

47.
Zhifeng, L., Yunyao, Y., Feng, W., Yongsheng, Z. and Ligang, C. (2013), "Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam", Struct. Eng. Mech.,48(5), 697-709. crossref(new window)