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Volumn 307, Issue 1-2, 2007, Pages 312-329

An artificial parameter-decomposition method for nonlinear oscillators: Applications to oscillators with odd nonlinearities

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONTROL NONLINEARITIES; DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; ITERATIVE METHODS; PARAMETER EXTRACTION; PERTURBATION TECHNIQUES;

EID: 34548299757     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.07.011     Document Type: Article
Times cited : (26)

References (69)
  • 3
    • 0036489498 scopus 로고    scopus 로고
    • Modified Linstedt-Poincare methods for some non-linear oscillations. Part I: expansion of constant
    • He J.H. Modified Linstedt-Poincare methods for some non-linear oscillations. Part I: expansion of constant. Journal of Non-Linear Mechanism 37 (2002) 309-314
    • (2002) Journal of Non-Linear Mechanism , vol.37 , pp. 309-314
    • He, J.H.1
  • 4
    • 33846210009 scopus 로고    scopus 로고
    • 1 / 3 force by He's modified Linstedt-Poincaré method
    • 1 / 3 force by He's modified Linstedt-Poincaré method. Journal of Sound and Vibration 301 (2007) 415-419
    • (2007) Journal of Sound and Vibration , vol.301 , pp. 415-419
    • Öziş, T.1    Yildirim2
  • 5
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.-H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics 20 (2006) 1141-1199
    • (2006) International Journal of Modern Physics , vol.20 , pp. 1141-1199
    • He, J.-H.1
  • 7
    • 0023648211 scopus 로고
    • Iteration procedure for determining approximate solutions to non-linear oscillator equations
    • Mickens R.E. Iteration procedure for determining approximate solutions to non-linear oscillator equations. Journal of Sound and Vibration 116 (1987) 185-187
    • (1987) Journal of Sound and Vibration , vol.116 , pp. 185-187
    • Mickens, R.E.1
  • 8
    • 33749265810 scopus 로고    scopus 로고
    • A classical iteration procedure valid for certain strongly nonlinear oscillators
    • Hu H., and Tang J.H. A classical iteration procedure valid for certain strongly nonlinear oscillators. Journal of Sound and Vibration 299 (2007) 397-402
    • (2007) Journal of Sound and Vibration , vol.299 , pp. 397-402
    • Hu, H.1    Tang, J.H.2
  • 9
    • 19944384579 scopus 로고    scopus 로고
    • A convolution integral method for certain strongly nonlinear oscillators
    • Hu H., and Tang J.H. A convolution integral method for certain strongly nonlinear oscillators. Journal of Sound and Vibration 285 (2005) 1235-1241
    • (2005) Journal of Sound and Vibration , vol.285 , pp. 1235-1241
    • Hu, H.1    Tang, J.H.2
  • 10
    • 24344480923 scopus 로고    scopus 로고
    • A generalized iteration procedure for calculating approximations to periodic solutions of "truly nonlinear oscillators"
    • Mickens R.E. A generalized iteration procedure for calculating approximations to periodic solutions of "truly nonlinear oscillators". Journal of Sound and Vibration 287 (2005) 1045-1051
    • (2005) Journal of Sound and Vibration , vol.287 , pp. 1045-1051
    • Mickens, R.E.1
  • 11
    • 0037058127 scopus 로고    scopus 로고
    • A modified Mickens procedure for certain non-linear oscillators
    • Lim C.W., and Wu B.S. A modified Mickens procedure for certain non-linear oscillators. Journal of Sound and Vibration 257 (2002) 202-206
    • (2002) Journal of Sound and Vibration , vol.257 , pp. 202-206
    • Lim, C.W.1    Wu, B.S.2
  • 12
    • 33644600306 scopus 로고    scopus 로고
    • 1 / 3 force oscillators, Journal of Sound and Vibration 292 (2006) 964-968.
  • 13
    • 33646517251 scopus 로고    scopus 로고
    • Solutions of nonlinear oscillators with fractional powers by an iterative procedure
    • Hu H. Solutions of nonlinear oscillators with fractional powers by an iterative procedure. Journal of Sound and Vibration 294 (2006) 608-614
    • (2006) Journal of Sound and Vibration , vol.294 , pp. 608-614
    • Hu, H.1
  • 14
    • 33745664224 scopus 로고    scopus 로고
    • A modified iteration perturbation method for some nonlinear oscillation problems
    • Marinca V., and Herinasu N. A modified iteration perturbation method for some nonlinear oscillation problems. Acta Mechanica 184 (2006) 231-242
    • (2006) Acta Mechanica , vol.184 , pp. 231-242
    • Marinca, V.1    Herinasu, N.2
  • 15
    • 33748424980 scopus 로고    scopus 로고
    • An analytical approximate technique for a class of strongly non-linear oscillators
    • Wu B.S., Sun W.P., and Lim C.W. An analytical approximate technique for a class of strongly non-linear oscillators. Journal of Non-Linear Mechanism 41 (2006) 766-774
    • (2006) Journal of Non-Linear Mechanism , vol.41 , pp. 766-774
    • Wu, B.S.1    Sun, W.P.2    Lim, C.W.3
  • 16
    • 0037412162 scopus 로고    scopus 로고
    • Analytical approximation to large-amplitude oscillation of a non-linear conservative system
    • Wu B.S., Lim C.W., and Ma Y.F. Analytical approximation to large-amplitude oscillation of a non-linear conservative system. Journal of Non-Linear Mechanism 38 (2003) 1037-1043
    • (2003) Journal of Non-Linear Mechanism , vol.38 , pp. 1037-1043
    • Wu, B.S.1    Lim, C.W.2    Ma, Y.F.3
  • 17
    • 0141882931 scopus 로고    scopus 로고
    • Large amplitude non-linear oscillations of a general conservative system
    • Wu B.S., and Lim C.W. Large amplitude non-linear oscillations of a general conservative system. Journal of Non-Linear Mechanism 39 (2004) 859-870
    • (2004) Journal of Non-Linear Mechanism , vol.39 , pp. 859-870
    • Wu, B.S.1    Lim, C.W.2
  • 18
    • 0035686567 scopus 로고    scopus 로고
    • A method for obtaining approximate analytic periods for a class of nonlinear oscillators
    • Wu B., and Li P. A method for obtaining approximate analytic periods for a class of nonlinear oscillators. Meccanica 36 (2001) 167-176
    • (2001) Meccanica , vol.36 , pp. 167-176
    • Wu, B.1    Li, P.2
  • 22
    • 0027911989 scopus 로고
    • A perturbation technique that works even when the non-linearity is not small
    • Senator M., and Bapat C.N. A perturbation technique that works even when the non-linearity is not small. Journal of Sound and Vibration 164 (1993) 1-27
    • (1993) Journal of Sound and Vibration , vol.164 , pp. 1-27
    • Senator, M.1    Bapat, C.N.2
  • 23
    • 20444380770 scopus 로고    scopus 로고
    • A generalization of the Senator-Bapat method for certain strongly nonlinear oscillators
    • Wu B.S., Lim C.W., and Li P.S. A generalization of the Senator-Bapat method for certain strongly nonlinear oscillators. Physics Letters A 341 (2005) 164-169
    • (2005) Physics Letters A , vol.341 , pp. 164-169
    • Wu, B.S.1    Lim, C.W.2    Li, P.S.3
  • 25
    • 15944389556 scopus 로고    scopus 로고
    • Improved Linstedt-Poincaré method for the solution of nonlinear problems
    • Amore P., and Aranda A. Improved Linstedt-Poincaré method for the solution of nonlinear problems. Journal of Sound and Vibration 283 (2005) 1115-1136
    • (2005) Journal of Sound and Vibration , vol.283 , pp. 1115-1136
    • Amore, P.1    Aranda, A.2
  • 26
    • 2942571550 scopus 로고    scopus 로고
    • High order analysis of nonlinear periodic differential equations
    • Amore P., and Lamas H.M. High order analysis of nonlinear periodic differential equations. Physics Letters A 327 (2004) 158-166
    • (2004) Physics Letters A , vol.327 , pp. 158-166
    • Amore, P.1    Lamas, H.M.2
  • 27
    • 1642616365 scopus 로고    scopus 로고
    • Presenting a new method for the solution of nonlinear problems
    • Amore P., and Aranda A. Presenting a new method for the solution of nonlinear problems. Physics Letters A 316 (2003) 218-225
    • (2003) Physics Letters A , vol.316 , pp. 218-225
    • Amore, P.1    Aranda, A.2
  • 28
    • 33751567742 scopus 로고    scopus 로고
    • Development of accurate solutions for a classical oscillator
    • Amore P., and Sanchez N.E. Development of accurate solutions for a classical oscillator. Journal of Sound and Vibration 283 (2007) 345-351
    • (2007) Journal of Sound and Vibration , vol.283 , pp. 345-351
    • Amore, P.1    Sanchez, N.E.2
  • 29
    • 19444376778 scopus 로고    scopus 로고
    • Comparison of alternative improved perturbative methods for nonlinear oscillations
    • Amore P., Raya A., and Fernández F.M. Comparison of alternative improved perturbative methods for nonlinear oscillations. Physics Letters A 340 (2005) 201-208
    • (2005) Physics Letters A , vol.340 , pp. 201-208
    • Amore, P.1    Raya, A.2    Fernández, F.M.3
  • 30
    • 0038394235 scopus 로고    scopus 로고
    • A. Pelster, H. Kleinert, M. Schanz, High order variational calculation for the frequency of time-periodic solutions, Physical Review E 67 (2003) 016604/1-6.
  • 35
    • 84907179772 scopus 로고    scopus 로고
    • J.I. Ramos, Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method, Chaos, Solitons and Fractals (2006), in press.
  • 36
    • 23644437348 scopus 로고    scopus 로고
    • Necessary conditions for the appearance of noise terms in decomposition series solutions
    • Wazwaz A.-M. Necessary conditions for the appearance of noise terms in decomposition series solutions. Applied Mathematics and Computation 81 (1997) 265-274
    • (1997) Applied Mathematics and Computation , vol.81 , pp. 265-274
    • Wazwaz, A.-M.1
  • 37
    • 0035311871 scopus 로고    scopus 로고
    • A computational algebraic investigation of the decomposition method for time-dependent problems
    • Lesnic D. A computational algebraic investigation of the decomposition method for time-dependent problems. Applied Mathematics and Computation 119 (2001) 197-206
    • (2001) Applied Mathematics and Computation , vol.119 , pp. 197-206
    • Lesnic, D.1
  • 40
    • 0037102888 scopus 로고    scopus 로고
    • On the order of convergence of Adomian method
    • Babolian E., and Biazar J. On the order of convergence of Adomian method. Applied Mathematic Computation 130 (2002) 383-387
    • (2002) Applied Mathematic Computation , vol.130 , pp. 383-387
    • Babolian, E.1    Biazar, J.2
  • 41
    • 0034553686 scopus 로고    scopus 로고
    • Convergence of Adomian's method applied to algebraic equations
    • Ouedraogo R.Z., Cherruault Y., and Abbaoui K. Convergence of Adomian's method applied to algebraic equations. Kybernetes 29 (2000) 1289-1305
    • (2000) Kybernetes , vol.29 , pp. 1289-1305
    • Ouedraogo, R.Z.1    Cherruault, Y.2    Abbaoui, K.3
  • 42
    • 0033240075 scopus 로고    scopus 로고
    • Convergence of Adomian's method applied to integral equations
    • Badredine T., Abbaoui K., and Cherruault Y. Convergence of Adomian's method applied to integral equations. Kybernetes 28 (1999) 557-564
    • (1999) Kybernetes , vol.28 , pp. 557-564
    • Badredine, T.1    Abbaoui, K.2    Cherruault, Y.3
  • 43
  • 46
    • 0035976505 scopus 로고    scopus 로고
    • Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs
    • Mandelzweig V.B., and Tabakin F. Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs. Computer Physics Communications 141 (2001) 268-281
    • (2001) Computer Physics Communications , vol.141 , pp. 268-281
    • Mandelzweig, V.B.1    Tabakin, F.2
  • 47
    • 0035879170 scopus 로고    scopus 로고
    • Numerical investigation of quasilinearization method in quantum mechanics
    • Krivec R., and Mandelzweig V.B. Numerical investigation of quasilinearization method in quantum mechanics. Computer Physics Communications 138 (2001) 69-79
    • (2001) Computer Physics Communications , vol.138 , pp. 69-79
    • Krivec, R.1    Mandelzweig, V.B.2
  • 48
    • 0037799370 scopus 로고    scopus 로고
    • Linearization methods in classical and quantum mechanics
    • Ramos J.I. Linearization methods in classical and quantum mechanics. Computer Physics Communications 153 (2003) 199-208
    • (2003) Computer Physics Communications , vol.153 , pp. 199-208
    • Ramos, J.I.1
  • 49
    • 24944528640 scopus 로고    scopus 로고
    • Piecewise-linearized methods for oscillators with limit cycles
    • Ramos J.I. Piecewise-linearized methods for oscillators with limit cycles. Chaos, Solitons and Fractals 27 (2006) 1229-1238
    • (2006) Chaos, Solitons and Fractals , vol.27 , pp. 1229-1238
    • Ramos, J.I.1
  • 50
    • 29144506145 scopus 로고    scopus 로고
    • Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods
    • Ramos J.I. Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods. Chaos, Solitons and Fractals 28 (2006) 1306-1313
    • (2006) Chaos, Solitons and Fractals , vol.28 , pp. 1306-1313
    • Ramos, J.I.1
  • 51
    • 33845965738 scopus 로고    scopus 로고
    • Piecewise-linearized methods for oscillators with fractional-power nonlinearities
    • Ramos J.I. Piecewise-linearized methods for oscillators with fractional-power nonlinearities. Journal of Sound and Vibration 300 (2007) 502-521
    • (2007) Journal of Sound and Vibration , vol.300 , pp. 502-521
    • Ramos, J.I.1
  • 52
    • 4243080805 scopus 로고    scopus 로고
    • Approximate period of nonlinear oscillators with discontinuities by modified Linstedt-Poincaré method
    • Liu H.-M. Approximate period of nonlinear oscillators with discontinuities by modified Linstedt-Poincaré method. Chaos, Solitons and Fractals 23 (2005) 577-579
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 577-579
    • Liu, H.-M.1
  • 53
    • 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. Journal of Computational and Applied Mathematics 207 (2007) 148-154
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , pp. 148-154
    • Xu, L.1
  • 54
    • 1642618653 scopus 로고    scopus 로고
    • A classical perturbation technique that works even when the linear part of restoring force is zero
    • Hu H. A classical perturbation technique that works even when the linear part of restoring force is zero. Journal of Sound and Vibration 271 (2004) 1175-1179
    • (2004) Journal of Sound and Vibration , vol.271 , pp. 1175-1179
    • Hu, H.1
  • 55
    • 3242733163 scopus 로고    scopus 로고
    • A modified method of equivalent linearization that works even when the non-linearity is not small
    • Hu H. A modified method of equivalent linearization that works even when the non-linearity is not small. Journal of Sound and Vibration 276 (2004) 1145-1149
    • (2004) Journal of Sound and Vibration , vol.276 , pp. 1145-1149
    • Hu, H.1
  • 56
    • 4644353662 scopus 로고    scopus 로고
    • Comparison of two Linstedt-Poincaré-type perturbation methods
    • Hu H., and Xiong Z.G. Comparison of two Linstedt-Poincaré-type perturbation methods. Journal of Sound and Vibration 278 (2004) 437-444
    • (2004) Journal of Sound and Vibration , vol.278 , pp. 437-444
    • Hu, H.1    Xiong, Z.G.2
  • 57
    • 0035850154 scopus 로고    scopus 로고
    • Mathematical and numerical study of the Duffing harmonic oscillator
    • Mickens R.E. Mathematical and numerical study of the Duffing harmonic oscillator. Journal of Sound and Vibration 244 (2001) 563-567
    • (2001) Journal of Sound and Vibration , vol.244 , pp. 563-567
    • Mickens, R.E.1
  • 58
    • 33646528864 scopus 로고    scopus 로고
    • Solution of a Duffing-harmonic oscillator by the method of harmonic balance
    • 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
    • (2006) Journal of Sound and Vibration , vol.294 , pp. 637-639
    • Hu, H.1    Tang, J.H.2
  • 60
    • 33748066633 scopus 로고    scopus 로고
    • Solutions of the Duffing-harmonic oscillator by an iteration procedure
    • Hu H. Solutions of the Duffing-harmonic oscillator by an iteration procedure. Journal of Sound and Vibration 298 (2006) 446-452
    • (2006) Journal of Sound and Vibration , vol.298 , pp. 446-452
    • Hu, H.1
  • 61
    • 0038294438 scopus 로고    scopus 로고
    • A new analytical approach to the Duffing-harmonic oscillator
    • Lim C.W., and Wu B.S. A new analytical approach to the Duffing-harmonic oscillator. Physics Letters A 311 (2003) 365-373
    • (2003) Physics Letters A , vol.311 , pp. 365-373
    • Lim, C.W.1    Wu, B.S.2
  • 62
    • 33745979117 scopus 로고    scopus 로고
    • Higher accuracy analytical approximations to the Duffing oscillator
    • Lim C.W., Wu B.S., and Sun W.P. Higher accuracy analytical approximations to the Duffing oscillator. Journal of Sound and Vibration 296 (2006) 1039-1045
    • (2006) Journal of Sound and Vibration , vol.296 , pp. 1039-1045
    • Lim, C.W.1    Wu, B.S.2    Sun, W.P.3
  • 64
    • 0037461472 scopus 로고    scopus 로고
    • Analysis of nonlinear oscillations in systems having non polynomial elastic terms
    • Mickens R.E. Analysis of nonlinear oscillations in systems having non polynomial elastic terms. Journal of Sound and Vibration 255 (2002) 789-792
    • (2002) Journal of Sound and Vibration , vol.255 , pp. 789-792
    • Mickens, R.E.1
  • 67
    • 0141905286 scopus 로고    scopus 로고
    • Harmonic balance based averaging: approximate realization of an asymptotic technique
    • Chatterjee A. Harmonic balance based averaging: approximate realization of an asymptotic technique. Nonlinear Dynamics 32 (2003) 323-343
    • (2003) Nonlinear Dynamics , vol.32 , pp. 323-343
    • Chatterjee, A.1
  • 69
    • 33846242561 scopus 로고    scopus 로고
    • 2) x = 0", Journal of Sound and Vibration 301 (2007) 427.


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