A new approach for solving a complex-valued differential equation

Journal of Sound and Vibration

Volumn 278, Issue 4-5, 2004, Pages 1181-1195

  Cveticanin, L ^a  

^a UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DAMPING; DEGREES OF FREEDOM (MECHANICS); FUNCTIONS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

BERNOULLI DIFFERENTIAL EQUATIONS; JACOBI ELLIPTIC FUNCTION; KRYLOV-BOGOLUBOV METHODS; NUMERICAL SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 6344237218     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2003.12.028     Document Type: Article

References (35)

1. Cveticanin L. Approximate analytical solutions to a class of non-linear equations with complex functions. Journal of Sound and Vibration. 157:1992;289-302.
2. Cveticanin L. An asymptotic solution for weak nonlinear vibrations of the rotor. Mechanism and Machine Theory. 28:1993;495-505.
3. Nayfeh A.H., Mook D.T. Nonlinear Oscillations. 1979;Wiley, New York.
4. N.N. Bogolubov, Y.A. Mitropolski, Asimptoticheskie metodi v teorii nelinejnih kolebanij, Fiz.mat.giz., Moscow, 1963.
5. Mahmoud G.M. Approximate solutions of a class of complex nonlinear dynamical systems. Physica A. 253:1998;211-222.
6. Yuste S.B., Bejarano D. Construction of approximate analytical solutions to a new class of non-linear oscillator equations. Journal of Sound and Vibration. 110:1986;347-350.
7. Yuste S.B., Bejarano D. Improvement of a Krylov-Bogolubov method that use Jacobi elliptic functions. Journal of Sound and Vibration. 139:1990;151-163.
8. Cheng S.H., Cheung Y.K. An elliptic perturbation method for certain strong non-linear oscillators. Journal of Sound and Vibration. 192:1996;453-464.
9. He J.H. A new perturbation technique which is also valid for large parameters. Journal of Sound and Vibration. 229:2000;1257-1263.
10. Belhaq M., Lakrad F. The elliptic multiple scales method for a class of autonomous strongly non-linear oscillators. Journal of Sound and Vibration. 234:2000;547-553.
11. Lakrad F., Belhaq M. Periodic solutions of strongly non-linear oscillators by the multiple scales method. Journal of Sound and Vibration. 258:2002;677-700.
12. Wu B., Zhong H. Application of vector-valued rational approximations to a class of non-linear oscillations. International Journal of Non-Linear Mechanics. 38:2003;249-254.
13. Mickens R.E. A generalization of the method of harmonic balance. Journal of Sound and Vibration. 111:1986;515-518.
14. Garcia-Margallo J., Bejarano J.D. A generalization of the method of harmonic balance. Journal of Sound and Vibration. 116:1987;591-595.
15. Coppola V.T., Rand R.H. Averaging using elliptic functions. approximation of limit cycles Acta Mechanica. 81:1990;125-142.
16. Belhaq M., Lakrad F. Prediction of homoclinic bifurcation. the elliptic averaging method Chaos, Solitons and Fractals. 11:2000;2251-2258.
17. Xu Z., Cheung Y.K. Averaging method using generalized harmonic functions for strongly non-linear oscillators. Journal of Sound and Vibration. 174:1994;563-576.
18. Vakakis A.F., Rand R.H. Normal modes and global dynamics of a two-degree-of-freedom non-linear system. Part I: low energies. International Journal of Non-linear Mechanics. 27:1992;861-874.
19. Vakakis A.F., Rand R.H. Normal modes and global dynamics of a two-degree-of-freedom non-linear system. Part II: high energies. International Journal of Non-linear Mechanics. 27:1992;874-884.
20. Cveticanin L. Analytical solutions of the system of two coupled pure cubic non-linear oscillators equations. Journal of Sound and Vibration. 245:2001;571-580.
21. Cveticanin L. Vibrations of a coupled two-degree-of-freedom system. Journal of Sound and Vibration. 247:2001;279-292.
22. Cveticanin L. The motion of a two mass system with non-linear connection. Journal of Sound and Vibration. 252:2002;361-369.
23. Cveticanin L. Forced non-linear vibrations of a symmetrical two-mass system. Journal of Sound and Vibration. 265:2003;451-458.
24. Cveticanin L. Vibrations of a free two-mass system with quadratic non-linearity and a constant excitation force. Journal of Sound and Vibration. 270:2004;441-449.
25. Genin J., Maybee J.S. External and material damped three dimensional rotor system. International Journal of Non-linear Mechanics. 5:1970;287-297.
26. A. Muszynska, On Rotor Dynamics, PAN, Warszaw, 1976.
27. Tondl A. Avtokolebanija Mehanicheskih Sistem. 1979;Mir, Moscow. (in Russian).
28. Cveticanin L. Analytical methods for solving strongly non-linear differential equations. Journal of Sound and Vibration. 214:1998;325-338.
29. Cveticanin L. Analytical approach for the solution of the complex valued strong non-linear differential equation of Duffing type. Physica A. 297:2001;348-360.
30. Cveticanin L. An approximate solution for a system of the coupled differential equations. Journal of Sound and Vibration. 152:1992;375-380.
31. Cveticanin L. Some particular solutions which describe the motion of the rotor. Journal of Sound and Vibration. 212:1998;173-178.
32. Manasevich R., Mawhin J., Zanolin F. Periodic solutions of some complex valued Liénard and Rayleigh equations. Nonlinear Analysis. 36:1999;997-1014.
33. Maccari A. Periodic and quasiperiodic motion for complex non-linear systems. International Journal of Non-linear Mechanics. 38:2003;575-584.
34. Byrd P.F., Friedman M.D. Handbook of Elliptic Integrals for Engineers and Physicists. 1954;Springer, Berlin.
35. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. 1979;Nauka, Moscow. (in Russian).