메뉴 건너뛰기




Volumn 22, Issue 4, 2013, Pages 532-537

Application of the harmonic balance method on nonlinear equations

Author keywords

Newton harmonic balance method; Nonlinear vibration; Oscillatory system; Time marching solution

Indexed keywords


EID: 84876892414     PISSN: 18184952     EISSN: 19916426     Source Type: Journal    
DOI: 10.5829/idosi.wasj.2013.22.04.532     Document Type: Article
Times cited : (13)

References (26)
  • 1
    • 33747332780 scopus 로고    scopus 로고
    • Theory and experiment on establishing the stability boundaries of a one-degree-of-freedom system under two high-frequency parametric excitation inputs
    • Yatawara, R.J., R.D. Neilson and A.D.S. Barr, 2006. Theory and experiment on establishing the stability boundaries of a one-degree-of-freedom system under two high-frequency parametric excitation inputs, Journal of Sound and Vibration, 297: 962-980.
    • (2006) Journal of Sound and Vibration , vol.297 , pp. 962-980
    • Yatawara, R.J.1    Neilson, R.D.2    Barr, A.D.S.3
  • 2
    • 0023090068 scopus 로고
    • Stability boundaries of an oscillator under high frequency multi-component parametric excitation
    • Othman, A.M., D. Watt and A.D.S. Barr, 1987. Stability boundaries of an oscillator under high frequency multi-component parametric excitation, Journal of Sound and Vibration, 112: 249-259.
    • (1987) Journal of Sound and Vibration , vol.112 , pp. 249-259
    • Othman, A.M.1    Watt, D.2    Barr, A.D.S.3
  • 3
    • 79953736761 scopus 로고    scopus 로고
    • An analytical approach to the Fornberg-Whitham type equations by using the variational iteration method
    • Junfeng Lu, 2011. An analytical approach to the Fornberg-Whitham type equations by using the variational iteration method, Computers and Mathematics with Applications, 61: 2010-2013.
    • (2011) Computers and Mathematics with Applications , vol.61 , pp. 2010-2013
    • Lu, J.1
  • 4
    • 79953748504 scopus 로고    scopus 로고
    • Variational iteration method and homotopy perturbation method for fourth-order fractionalintegro-differential equations
    • Yasir Nawaz, 2011. Variational iteration method and homotopy perturbation method for fourth-order fractionalintegro-differential equations, Computers and Mathematics with Applications, 61: 2330-2341.
    • (2011) Computers and Mathematics with Applications , vol.61 , pp. 2330-2341
    • Nawaz, Y.1
  • 6
    • 56049098395 scopus 로고    scopus 로고
    • Investigation of a powerful analytical method into natural convection boundary layer flow, Commun Nonlinear Sci
    • Abdoul R. Ghotbi, H. Bararnia, G. Domairry and A. Barari, 2009. Investigation of a powerful analytical method into natural convection boundary layer flow, Commun Nonlinear Sci. Numer Simulat, 14: 2222-2228.
    • (2009) Numer Simulat , vol.14 , pp. 2222-2228
    • Ghotbi, A.R.1    Bararnia, H.2    Domairry, G.3    Barari, A.4
  • 7
    • 74449092463 scopus 로고    scopus 로고
    • Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux, Commun Nonlinear Sci
    • Sohouli, A.R., M. Famouri, A. Kimiaeifar and G. Domairry, 2010. Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux, Commun Nonlinear Sci. Numer Simulat., 15: 1691-1699.
    • (2010) Numer Simulat. , vol.15 , pp. 1691-1699
    • Sohouli, A.R.1    Famouri, M.2    Kimiaeifar, A.3    Domairry, G.4
  • 9
    • 79953212593 scopus 로고    scopus 로고
    • Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods
    • Farrokhzad, F., P. Mowlaee, A. Barari, A.J. Choobbasti and H.D. Kaliji, 2011. Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods, Carpathian Journal of Mathematics, 27(1): 51-63.
    • (2011) Carpathian Journal of Mathematics , vol.27 , Issue.1 , pp. 51-63
    • Farrokhzad, F.1    Mowlaee, P.2    Barari, A.3    Choobbasti, A.J.4    Kaliji, H.D.5
  • 10
    • 78650881841 scopus 로고    scopus 로고
    • The fractional variational iteration method using He's polynomials
    • Shimin Guo, Liquan Mei, The fractional variational iteration method using He's polynomials, Physics Letters A. 375 (2011) 309-313.
    • (2011) Physics Letters A. , vol.375 , pp. 309-313
    • Guo, S.1    Mei, L.2
  • 12
    • 81555211356 scopus 로고    scopus 로고
    • Analytical Solutions for Investigating Free Vibration of Cantilever Beams
    • Kaliji, H.D., A. Fereidoon, M. Ghadimi and M. Eftari, 2010. Analytical Solutions for Investigating Free Vibration of Cantilever Beams, World Applied Sciences Journal, 9(Special Issue of Applied Math): 44-48.
    • (2010) World Applied Sciences Journal , vol.9 , Issue.SPEC. ISSUE , pp. 44-48
    • Kaliji, H.D.1    Fereidoon, A.2    Ghadimi, M.3    Eftari, M.4
  • 15
    • 70350573456 scopus 로고    scopus 로고
    • He's frequency-amplitude formulation for nonlinear oscillators with an irrational force
    • Zhao Ling, 2009. He's frequency-amplitude formulation for nonlinear oscillators with an irrational force, Computers and Mathematics with Applications, 58: 2477-2479.
    • (2009) Computers and Mathematics with Applications , vol.58 , pp. 2477-2479
    • Ling, Z.1
  • 16
    • 47049099601 scopus 로고    scopus 로고
    • He, Max-min approach to nonlinear oscillators, Int
    • Ji-Huan, 2008. He, Max-min approach to nonlinear oscillators, Int. J. Nonlinear Sci. Numer. Simul., 9(2): 207-210.
    • (2008) J. Nonlinear Sci. Numer. Simul. , vol.9 , Issue.2 , pp. 207-210
    • Ji-Huan1
  • 18
    • 34748902823 scopus 로고    scopus 로고
    • Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method
    • Turgut Özis and Ahmet Yíldirim, 2007. Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method. Computers and Mathematics with Applications, 54: 1184-1187.
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 1184-1187
    • Özis, T.1    Yíldirim, A.2
  • 19
    • 84863009060 scopus 로고    scopus 로고
    • Nonlinear vibration of oscillation systems using frequency amplitude formulation
    • DOI: 10.3233/SAV20100633 In Press
    • Fereidoon, A., M. Ghadimi, A. Barari, H.D. Kaliji and G. Domairry, 2011. Nonlinear vibration of oscillation systems using frequency amplitude formulation, Shock and Vibration, 18: 1-10, DOI:10.3233/SAV20100633 In Press.
    • (2011) Shock and Vibration , vol.18 , pp. 1-10
    • Fereidoon, A.1    Ghadimi, M.2    Barari, A.3    Kaliji, H.D.4    Domairry, G.5
  • 20
    • 43049085115 scopus 로고    scopus 로고
    • Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable
    • Beléndez, A., D.I. Méndez, T. Beléndez, A. Hernández and M.L. Álvarez, 2008. Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable, Journal of Sound and Vibration, 314: 775-782.
    • (2008) Journal of Sound and Vibration , vol.314 , pp. 775-782
    • Beléndez, A.1    Méndez, D.I.2    Beléndez, T.3    Hernández, A.4    Álvarez, M.L.5
  • 21
    • 33748424980 scopus 로고    scopus 로고
    • An analytical approximate technique for a class of strongly non-linear oscillators
    • Wu, B.S., W.P. Sun and C.W. Lim, 2006. An analytical approximate technique for a class of strongly non-linear oscillators, International Journal of Non-Linear Mechanics, 41: 766-774.
    • (2006) International Journal of Non-Linear Mechanics , vol.41 , pp. 766-774
    • Wu, B.S.1    Sun, W.P.2    Lim, C.W.3
  • 22
    • 54049138060 scopus 로고    scopus 로고
    • Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic Duffing oscillators
    • Lai, S.K., C.W. Lim, B.S. Wu, C. Wang, Q.C. Zeng and X.F. He, 2009. Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic Duffing oscillators, Applied Mathematical Modelling. 33: 852-866.
    • (2009) Applied Mathematical Modelling. , vol.33 , pp. 852-866
    • Lai, S.K.1    Lim, C.W.2    Wu, B.S.3    Wang, C.4    Zeng, Q.C.5    He, X.F.6
  • 23
    • 77957955886 scopus 로고    scopus 로고
    • Analysis of highly nonlinear oscillation systems using He's max-min method and comparison with homotopy analysis and energy balance methods
    • Ibsen, L.B., A. Barari and A. Kimiaeifar, 2010. Analysis of highly nonlinear oscillation systems using He's max-min method and comparison with homotopy analysis and energy balance methods, Sadhana, 35: 1-16.
    • (2010) Sadhana , vol.35 , pp. 1-16
    • Ibsen, L.B.1    Barari, A.2    Kimiaeifar, A.3
  • 25
    • 0035850154 scopus 로고    scopus 로고
    • Mathematical and numerical study of the Duffing-harmonic oscillator
    • Mickens, R.E., 2001. Mathematical and numerical study of the Duffing-harmonic oscillator, Journal of Sound and Vibration, 244(3): 563-567.
    • (2001) Journal of Sound and Vibration , vol.244 , Issue.3 , pp. 563-567
    • Mickens, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.