메뉴 건너뛰기




Volumn 41, Issue 2, 2009, Pages 642-645

Frequency-amplitude relationship of nonlinear oscillators by He's parameter-expanding method

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES;

EID: 67349260734     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2008.02.036     Document Type: Article
Times cited : (21)

References (33)
  • 1
    • 33748922411 scopus 로고    scopus 로고
    • Non-perturbative methods for strongly nonlinear problems
    • dissertation. Berlin: de-Verlag im Internet GmbH;
    • He JH. Non-perturbative methods for strongly nonlinear problems, dissertation. Berlin: de-Verlag im Internet GmbH; 2006.
    • (2006)
    • He, J.H.1
  • 2
    • 34250213225 scopus 로고    scopus 로고
    • Variational approach for nonlinear oscillators
    • He J.H. Variational approach for nonlinear oscillators. Chaos, Solitons & Fractals 34 5 (2007) 1430-1439
    • (2007) Chaos, Solitons & Fractals , vol.34 , Issue.5 , pp. 1430-1439
    • He, J.H.1
  • 3
    • 0036526626 scopus 로고    scopus 로고
    • Preliminary report on the energy balance for nonlinear oscillations
    • He J.H. Preliminary report on the energy balance for nonlinear oscillations. Mech Res Commun 29 (2002) 107-111
    • (2002) Mech Res Commun , vol.29 , pp. 107-111
    • He, J.H.1
  • 4
    • 4444377082 scopus 로고    scopus 로고
    • Determination of limit cycles for strongly nonlinear oscillators
    • Art. No. 174301
    • He J.H. Determination of limit cycles for strongly nonlinear oscillators. Phys Rev Lett 90 17 (2003) Art. No. 174301
    • (2003) Phys Rev Lett , vol.90 , Issue.17
    • He, J.H.1
  • 5
    • 26444442005 scopus 로고    scopus 로고
    • Determination of limit cycles for a modified van der Pol oscillator
    • D'Acunto M. Determination of limit cycles for a modified van der Pol oscillator. Mech Res Commun 33 (2006) 93-98
    • (2006) Mech Res Commun , vol.33 , pp. 93-98
    • D'Acunto, M.1
  • 6
    • 0041621600 scopus 로고    scopus 로고
    • Variational principles for some nonlinear partial differential equations with variable coefficients
    • He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons & Fractals 19 4 (2004) 847-851
    • (2004) Chaos, Solitons & Fractals , vol.19 , Issue.4 , pp. 847-851
    • He, J.H.1
  • 7
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method-a kind of nonlinear analytical technique
    • He J.H. Variational iteration method-a kind of nonlinear analytical technique. Int J Nonlinear Mech 34 4 (1999) 699-708
    • (1999) Int J Nonlinear Mech , vol.34 , Issue.4 , pp. 699-708
    • He, J.H.1
  • 8
    • 33748293091 scopus 로고    scopus 로고
    • Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives
    • Art. No. 082902
    • Draganescu G.E. Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives. J Math Phys 47 8 (2006) Art. No. 082902
    • (2006) J Math Phys , vol.47 , Issue.8
    • Draganescu, G.E.1
  • 9
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int J Nonlinear Sci Numer Simulat 7 1 (2006) 27-34
    • (2006) Int J Nonlinear Sci Numer Simulat , vol.7 , Issue.1 , pp. 27-34
    • Odibat, Z.M.1    Momani, S.2
  • 10
    • 32644457439 scopus 로고    scopus 로고
    • The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations
    • Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations. Int J Nonlinear Sci Numer Simulat 7 1 (2006) 65-70
    • (2006) Int J Nonlinear Sci Numer Simulat , vol.7 , Issue.1 , pp. 65-70
    • Bildik, N.1    Konuralp, A.2
  • 11
    • 34249883978 scopus 로고    scopus 로고
    • Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations
    • Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. Int J Nonlinear Sci Numer Simulat 8 2 (2007) 152-158
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.2 , pp. 152-158
    • Yusufoglu, E.1
  • 12
    • 34249893388 scopus 로고    scopus 로고
    • Approximate solutions of K(2, 2), K dV and modified K dV equations by variational iteration method, homotopy perturbation method and homotopy analysis method
    • Tari H., Ganji D.D., and Rostamian M. Approximate solutions of K(2, 2), K dV and modified K dV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. Int J Nonlinear Sci Numer Simulat 8 2 (2007) 203-210
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.2 , pp. 203-210
    • Tari, H.1    Ganji, D.D.2    Rostamian, M.3
  • 13
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 1 (2004) 287-292
    • (2004) Appl Math Comput , vol.151 , Issue.1 , pp. 287-292
    • He, J.H.1
  • 14
    • 18844391045 scopus 로고    scopus 로고
    • Limit cycle and bifurcation of nonlinear problems
    • He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons & Fractals 26 (2005) 827-833
    • (2005) Chaos, Solitons & Fractals , vol.26 , pp. 827-833
    • He, J.H.1
  • 15
    • 17844387391 scopus 로고    scopus 로고
    • Homotopy perturbation method for bifurcation of nonlinear problems
    • He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlinear Sci Numer Simulat 6 2 (2005) 207-208
    • (2005) Int J Nonlinear Sci Numer Simulat , vol.6 , Issue.2 , pp. 207-208
    • He, J.H.1
  • 16
    • 32644482553 scopus 로고    scopus 로고
    • Approximate period solution for a kind of nonlinear oscillator by He's perturbation method
    • Cai X.C., Wu W.Y., and Li M.S. Approximate period solution for a kind of nonlinear oscillator by He's perturbation method. Int J Nonlinear Sci Numer Simulat 7 (2006) 109-112
    • (2006) Int J Nonlinear Sci Numer Simulat , vol.7 , pp. 109-112
    • Cai, X.C.1    Wu, W.Y.2    Li, M.S.3
  • 17
    • 33745852188 scopus 로고    scopus 로고
    • Homotopy-perturbation method for pure nonlinear differential equation
    • Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos, Solitons & Fractals 30 5 (2006) 1221-1230
    • (2006) Chaos, Solitons & Fractals , vol.30 , Issue.5 , pp. 1221-1230
    • Cveticanin, L.1
  • 18
    • 34249898148 scopus 로고    scopus 로고
    • Application of He's homotopy perturbation method to the Duffing-harmonic oscillator
    • Beléndez A., Hernández T., Beléndez, et al. Application of He's homotopy perturbation method to the Duffing-harmonic oscillator. Int J Nonlinear Sci Numer Simulat 8 1 (2007) 79-88
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.1 , pp. 79-88
    • Beléndez, A.1    Hernández, T.2    Beléndez3
  • 19
    • 34249910643 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to squeezing flow of a newtonian fluid
    • Ghori Q.K., Ahmed M., and Siddiqui A.M. Application of homotopy perturbation method to squeezing flow of a newtonian fluid. Int J Nonlinear Sci Numer Simulat 8 2 (2007) 179-184
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.2 , pp. 179-184
    • Ghori, Q.K.1    Ahmed, M.2    Siddiqui, A.M.3
  • 21
    • 34249865652 scopus 로고    scopus 로고
    • He's homotopy perturbation method for calculating adomian polynomials
    • Ghorbani A., and Saberi-Nadjafi J. He's homotopy perturbation method for calculating adomian polynomials. Int J Nonlinear Sci Numer Simulat 2 (2007) 229-232
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.2 , pp. 229-232
    • Ghorbani, A.1    Saberi-Nadjafi, J.2
  • 22
    • 34249884542 scopus 로고    scopus 로고
    • Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method
    • Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method. Int J Nonlinear Sci Numer Simulat 8 2 (2007) 239-242
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.2 , pp. 239-242
    • Öziş, T.1    Yildirim, A.2
  • 23
    • 34249884541 scopus 로고    scopus 로고
    • A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities
    • Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. Int J Nonlinear Sci Numer Simulat 8 2 (2007) 243-248
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.2 , pp. 243-248
    • Öziş, T.1    Yildirim, A.2
  • 24
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30 3 (2006) 700-708
    • (2006) Chaos, Solitons & Fractals , vol.30 , Issue.3 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 25
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 10 (2006) 1141-1199
    • (2006) Int J Mod Phys B , vol.20 , Issue.10 , pp. 1141-1199
    • He, J.H.1
  • 26
    • 0035601179 scopus 로고    scopus 로고
    • Bookkeeping parameter in perturbation methods
    • He J.H. Bookkeeping parameter in perturbation methods. Int J Nonlinear Sci Numer Simulat 2 3 (2001) 257-264
    • (2001) Int J Nonlinear Sci Numer Simulat , vol.2 , Issue.3 , pp. 257-264
    • He, J.H.1
  • 27
    • 0036489498 scopus 로고    scopus 로고
    • Modified Lindsted-Poincare methods for some strongly nonlinear oscillations, Part I: expansion of a constant
    • He J.H. Modified Lindsted-Poincare methods for some strongly nonlinear oscillations, Part I: expansion of a constant. Int J Nonlinear Mech 37 2 (2002) 309-314
    • (2002) Int J Nonlinear Mech , vol.37 , Issue.2 , pp. 309-314
    • He, J.H.1
  • 28
    • 33746584753 scopus 로고    scopus 로고
    • New interpretation of homotopy-perturbation method
    • He J.H. New interpretation of homotopy-perturbation method. Int J Mod Phys B 20 18 (2006) 2561-2568
    • (2006) Int J Mod Phys B , vol.20 , Issue.18 , pp. 2561-2568
    • He, J.H.1
  • 29
    • 34250663068 scopus 로고    scopus 로고
    • He's parameter expanding methods for strongly nonlinear oscillators
    • Xu L. He's parameter expanding methods for strongly nonlinear oscillators. J Comput Appl Math 207 1 (2007) 148-154
    • (2007) J Comput Appl Math , vol.207 , Issue.1 , pp. 148-154
    • Xu, L.1
  • 30
    • 33846784840 scopus 로고    scopus 로고
    • Determination of limit cycle by He's parameter expanding method for strongly nonlinear oscillators
    • Xu L. Determination of limit cycle by He's parameter expanding method for strongly nonlinear oscillators. J Sound Vibrat 302 (2007) 178-184
    • (2007) J Sound Vibrat , vol.302 , pp. 178-184
    • Xu, L.1
  • 31
    • 4243080805 scopus 로고    scopus 로고
    • Approximate period of nonlinear oscillators with discontinuities by modified Lindsted-Poincare method
    • Liu H.M. Approximate period of nonlinear oscillators with discontinuities by modified Lindsted-Poincare method. Chaos, Solitons & Fractals 23 2 (2005) 577-579
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.2 , pp. 577-579
    • Liu, H.M.1
  • 32
    • 34547661887 scopus 로고    scopus 로고
    • Application of He's parameter expansion method to an oscillation of a mass attached to a stretched elastic wire
    • Xu L. Application of He's parameter expansion method to an oscillation of a mass attached to a stretched elastic wire. Phys Lett A 368 3-4 (2007) 259-262
    • (2007) Phys Lett A , vol.368 , Issue.3-4 , pp. 259-262
    • Xu, L.1
  • 33
    • 34249996463 scopus 로고    scopus 로고
    • Application of parameter expanding method to strongly nonlinear oscillators
    • Da-Hua S., and He J.H. Application of parameter expanding method to strongly nonlinear oscillators. Int J Nonlinear Sci Numer Simulat 8 1 (2007) 121-124
    • (2007) Int J Nonlinear Sci Numer Simulat , vol.8 , Issue.1 , pp. 121-124
    • Da-Hua, S.1    He, J.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.