Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable

Journal of Sound and Vibration

Volumn 314, Issue 3-5, 2008, Pages 775-782

  Belendez A ^a   Mendez D I ^a   Belendez T ^a   Hernandez A ^a   Alvarez M L ^a  

^a UNIVERSITY OF ALICANTE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; OSCILLATORS (MECHANICAL); PROBLEM SOLVING;

HARMONIC BALANCE; NONLINEAR DIFFERENTIAL EQUATION; NONLINEAR OSCILLATORS; RESTORING FORCE;

HARMONIC GENERATION;

EID: 43049085115     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2008.01.021     Document Type: Article

References (26)

1. -1=0. Journal of Sound and Vibration 306 (2007) 968-972
2. Acton J.R., and Squire P.T. Solving Equations with Physical Understanding (1985), Adam Hilger, Bristol and Boston (Chapter 5)
3. Mickens R.E. Oscillations in Planar Dynamics Systems (1996), World Scientific, Singapore
4. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 10 (2006) 1141-1199
5. Nayfeh A.H. Problems in Perturbations (1985), Wiley, New York
6. He J.H. Modified Lindstedt-Poincare methods for some non-linear oscillations. Part I: expansion of a constant. International Journal of Non-linear Mechanics 37 (2002) 309-314
7. 1/3 force by He's modified Lindstedt-Poincaré method. Journal of Sound and Vibration 301 (2007) 415-419
8. Shou D.H., and He J.H. Application of parameter-expanding method to strongly nonlinear oscillators. International Journal of Nonlinear Sciences and Numerical Simulation 8 1 (2007) 121-124
9. He J.H. Homotopy perturbation method for bifurcation on nonlinear problems. International Journal of Nonlinear Sciences and Numerical Simulation. 6 (2005) 207-208
10. Shakeri F., and Dehghan M. Inverse problem of diffusion by He's homotopy perturbation method. Physica Scripta 75 (2007) 551-556
11. Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 4 (2006) 411-418
12. Beléndez A., Hernández A., Beléndez T., and Márquez A. Application of the homotopy perturbation method to the nonlinear pendulum. European Journal of Physics 28 (2007) 93-104
13. Beléndez A., Hernández A., Beléndez T., Fernández E., Álvarez M.L., and Neipp C. Application of He's homotopy perturbation method to the Duffing-harmonic oscillator. International Journal of Nonlinear Sciences and Numerical Simulation 8 1 (2007) 79-88
14. Chowdhury M.S.H., and Hashim I. Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Physics Letters A 365 (2007) 439-447
15. Özis T., and Yildirim A. A comparative Study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 243-248
16. Amore P., and Aranda A. Improved Lindstedt-Poincaré method for the solution of nonlinear problems. Journal of Sound and Vibration 283 (2005) 1115-1136
17. Amore P., and Fernández F.M. Exact and approximate expressions for the period of anharmonic oscillators. European Journal of Physics 26 (2005) 589-601
18. Amore P., Raya A., and Fernández F.M. Alternative perturbation approaches in classical mechanics. European Journal of Physics 26 (2005) 1057-1063
19. Wu B.S., and Lim C.W. Large amplitude nonlinear oscillations of a general conservative system. International Journal of Non-linear Mechanics 39 (2004) 859-870
20. Lim C.W., and Wu B.S. Accurate higher-order approximations to frequencies of nonlinear oscillators with fractional powers. Journal of Sound and Vibration 281 (2005) 1157-1162
21. Lim C.W., and Wu B.S. A new analytical approach to the Duffing-harmonic oscillator. Physics Letters A 311 (2003) 365-373
22. Beléndez A., Hernández A., Márquez A., Beléndez T., and Neipp C. Analytical approximations for the period of a simple pendulum. European Journal of Physics 27 (2006) 539-551
23. Hu H., and Tang J.H. Solution of a Duffing-harmonic oscillator by the method of harmonic balance. Journal of Sound and Vibration 294 (2006) 637-639
24. Beléndez A., and Pascual C. Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator. Physics Letters A 371 (2007) 291-299
25. Beléndez A., Hernández A., Beléndez T., Álvarez M.L., Gallego S., Ortuño M., and Neipp C. Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire. Journal of Sound and Vibration 302 (2007) 1018-1029
26. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1972), Dover, New York pp. 258, 263