메뉴 건너뛰기




Volumn 307, Issue 3-5, 2007, Pages 720-736

Accurate approximate analytical solutions for nonlinear free vibration of systems with serial linear and nonlinear stiffness

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; LINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; STIFFNESS; VIBRATION ANALYSIS;

EID: 34548583484     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.06.061     Document Type: Article
Times cited : (23)

References (34)
  • 2
    • 84907185894 scopus 로고    scopus 로고
    • N. Minorsky, Nonlinear Oscillations, Huntington, R.E. Krieger, New York, 1974.
  • 5
    • 0003897780 scopus 로고
    • Clarendon, Oxford (translated by Wolfram Stadler)
    • Hagedorn P. Non-linear Oscillations (1988), Clarendon, Oxford (translated by Wolfram Stadler)
    • (1988) Non-linear Oscillations
    • Hagedorn, P.1
  • 7
    • 0022894477 scopus 로고
    • A generalization of the method of harmonic balance
    • Mickens R.E. A generalization of the method of harmonic balance. Journal of Sound and Vibration 111 (1986) 515-518
    • (1986) Journal of Sound and Vibration , vol.111 , pp. 515-518
    • Mickens, R.E.1
  • 8
    • 0001241171 scopus 로고
    • Nonperturbative (but approximate) method for solving differential equations and finding limit cycles
    • Delamotte B. Nonperturbative (but approximate) method for solving differential equations and finding limit cycles. Physical Review Letters 70 (1993) 3361-3364
    • (1993) Physical Review Letters , vol.70 , pp. 3361-3364
    • Delamotte, B.1
  • 9
    • 38149146318 scopus 로고
    • Some remarks of the harmonic balance method for mixed-parity non-linear oscillations
    • Venkateshwar Rao A., and Nageswara Rao B. Some remarks of the harmonic balance method for mixed-parity non-linear oscillations. Journal of Sound and Vibration 170 (1994) 571-576
    • (1994) Journal of Sound and Vibration , vol.170 , pp. 571-576
    • Venkateshwar Rao, A.1    Nageswara Rao, B.2
  • 11
    • 0037468846 scopus 로고    scopus 로고
    • Frequencies of oscillators with fractional-power non-linearities
    • Gottlieb H.P.W. Frequencies of oscillators with fractional-power non-linearities. Journal of Sound and Vibration 261 (2003) 557-566
    • (2003) Journal of Sound and Vibration , vol.261 , pp. 557-566
    • Gottlieb, H.P.W.1
  • 12
    • 0035650191 scopus 로고    scopus 로고
    • A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation
    • Lim C.W., Wu B.S., and He L.H. A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation. Chaos 11 (2001) 843-848
    • (2001) Chaos , vol.11 , pp. 843-848
    • Lim, C.W.1    Wu, B.S.2    He, L.H.3
  • 13
    • 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
  • 14
    • 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
  • 15
    • 0022043580 scopus 로고
    • Weighted linearization technique for period approximation in large amplitude nonlinear oscillations
    • Agrwal V.P., and Denman H.H. Weighted linearization technique for period approximation in large amplitude nonlinear oscillations. Journal of Sound and Vibration 99 (1985) 463-473
    • (1985) Journal of Sound and Vibration , vol.99 , pp. 463-473
    • Agrwal, V.P.1    Denman, H.H.2
  • 16
    • 0025887981 scopus 로고
    • A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
    • Cheung Y.K., Chen S.H., and Lau S.L. A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators. International Journal of Non-linear Mechanics 26 (1991) 367-378
    • (1991) International Journal of Non-linear Mechanics , vol.26 , pp. 367-378
    • Cheung, Y.K.1    Chen, S.H.2    Lau, S.L.3
  • 17
    • 0030567896 scopus 로고    scopus 로고
    • A power series approach for the study of periodic motion
    • Qaisi M.I. A power series approach for the study of periodic motion. Journal of Sound and Vibration 196 (1996) 401-406
    • (1996) Journal of Sound and Vibration , vol.196 , pp. 401-406
    • Qaisi, M.I.1
  • 19
    • 33644517521 scopus 로고    scopus 로고
    • Free vibrations of a mass grounded by linear and nonlinear springs in series
    • Telli S., and Kopmaz O. Free vibrations of a mass grounded by linear and nonlinear springs in series. Journal of Sound and Vibration 289 (2006) 689-710
    • (2006) Journal of Sound and Vibration , vol.289 , pp. 689-710
    • Telli, S.1    Kopmaz, O.2
  • 20
    • 0035686567 scopus 로고    scopus 로고
    • A method for obtaining approximate analytic periods for a class of nonlinear oscillators
    • Wu B.S., and Li P.S. 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.S.1    Li, P.S.2
  • 21
    • 0041845048 scopus 로고    scopus 로고
    • A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations
    • Mickens R.E. A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations. Journal of Sound and Vibration 264 (2003) 1195-1200
    • (2003) Journal of Sound and Vibration , vol.264 , pp. 1195-1200
    • Mickens, R.E.1
  • 22
    • 0000987662 scopus 로고    scopus 로고
    • New approaches for the study of non-linear oscillators
    • Iyengar R.N., and Roy D. New approaches for the study of non-linear oscillators. Journal of Sound and Vibration 211 (1998) 843-875
    • (1998) Journal of Sound and Vibration , vol.211 , pp. 843-875
    • Iyengar, R.N.1    Roy, D.2
  • 23
    • 0000987661 scopus 로고    scopus 로고
    • Extensions of the phase space linearization (PSL) technique for non-linear oscillators
    • Iyengar R.N., and Roy D. Extensions of the phase space linearization (PSL) technique for non-linear oscillators. Journal of Sound and Vibration 211 (1998) 877-906
    • (1998) Journal of Sound and Vibration , vol.211 , pp. 877-906
    • Iyengar, R.N.1    Roy, D.2
  • 24
    • 0001262334 scopus 로고    scopus 로고
    • Classical and quantum oscillations of quartic anharmonicities: second-order solution
    • Pathak A., and Mandal S. Classical and quantum oscillations of quartic anharmonicities: second-order solution. Physics Letters A 286 (2001) 261-276
    • (2001) Physics Letters A , vol.286 , pp. 261-276
    • Pathak, A.1    Mandal, S.2
  • 26
    • 9544240343 scopus 로고    scopus 로고
    • On the modified Taylor's approximation for the solution of linear and nonlinear equations
    • Bulos B., and Khuri S.A. On the modified Taylor's approximation for the solution of linear and nonlinear equations. Applied Mathematics and Computation 160 (2005) 939-953
    • (2005) Applied Mathematics and Computation , vol.160 , pp. 939-953
    • Bulos, B.1    Khuri, S.A.2
  • 27
    • 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
  • 28
    • 0030214603 scopus 로고    scopus 로고
    • Fourier analysis of a rational harmonic balance approximation for periodic solutions
    • Mickens R.E., and Semwogerere D. Fourier analysis of a rational harmonic balance approximation for periodic solutions. Journal of Sound and Vibration 195 (1996) 528-530
    • (1996) Journal of Sound and Vibration , vol.195 , pp. 528-530
    • Mickens, R.E.1    Semwogerere, D.2
  • 29
    • 0037411939 scopus 로고    scopus 로고
    • Comparison of Fourier sine and cosine series expansions for beams with arbitrary boundary conditions
    • Li W.L. Comparison of Fourier sine and cosine series expansions for beams with arbitrary boundary conditions. Journal of Sound and Vibration 255 (2002) 185-194
    • (2002) Journal of Sound and Vibration , vol.255 , pp. 185-194
    • Li, W.L.1
  • 31
    • 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. International Journal of Non-linear Mechanics 39 (2004) 859-870
    • (2004) International Journal of Non-linear Mechanics , vol.39 , pp. 859-870
    • Wu, B.S.1    Lim, C.W.2
  • 32
    • 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. International Journal of Non-linear Mechanics 38 (2003) 1037-1043
    • (2003) International Journal of Non-linear Mechanics , vol.38 , pp. 1037-1043
    • Wu, B.S.1    Lim, C.W.2    Ma, Y.F.3
  • 33
    • 0037769060 scopus 로고    scopus 로고
    • A new method for approximate analytical solutions to nonlinear oscillations of nonnatural systems
    • Wu B.S., Lim C.W., and He L.H. A new method for approximate analytical solutions to nonlinear oscillations of nonnatural systems. Nonlinear Dynamics 32 (2003) 1-13
    • (2003) Nonlinear Dynamics , vol.32 , pp. 1-13
    • Wu, B.S.1    Lim, C.W.2    He, L.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.