Periodic solutions of the Duffing equation

Structural Engineering and Mechanics

Volumn 30, Issue 5, 2008, Pages 593-602

  Tezcan, Jale ^a   Hsiao, J Kent ^a  

^a Southern Illinois University at Carbondale   (United States)

Author keywords

Duffing equation; Harmonic balance method; Linearization; Nonlinear oscillator

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HARMONIC ANALYSIS; LINEARIZATION; NONLINEAR EQUATIONS; NUMERICAL METHODS;

COMPUTATIONALLY EFFICIENT; DUFFING EQUATIONS; FREQUENCY COMPONENTS; HARMONIC BALANCE METHOD; NON-LINEAR OSCILLATORS; NUMERICAL INTEGRATIONS; REGION OF CONVERGENCE; SINGLE DEGREE OF FREEDOM SYSTEMS;

RUNGE KUTTA METHODS;

EID: 56649100420     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2008.30.5.593     Document Type: Article

References (11)

1. Caughey, T.K. (1963), "Equivalent linearization techniques", J. Acoust. Soc. Am., 35(11), 1706-1711.
2. Caughey, T.K. (1971), "Nonlinear theory of random vibrations", Adv. Appl. Mech., 11, 209-253.
3. Iwan, W.D. (1969), "On defining equivalent systems for certain ordinary nonlinear differential equations", Int. J. Nonlinear Mech., 4, 325-334.
4. Jordan, D.W. and P. Smith (1999), "Nonlinear ordinary differential equations: An introduction to dynamical systems", Oxford University Press.
5. Krylov, N.N. and N.N. Bogoliubov (1947), Introduction to Nonlinear Mechanics. Princeton University, Princeton.
6. Liu, L., J.P. Thomas, et al. (2006), "A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator", J. Comput. Phys., 215(1), 298-320.
7. Nayfeh, A.H. and D.T. Mook (1979), Nonlinear Oscillations, John Wiley, New York.
8. Roberts, J. and P.D. Spanos (1986), Random Vibration and Statistical Linearization, Wiley, New York.
9. Spanos, P.D. and W.D. Iwan (1978), "On the existence and uniqueness of solutions generated by equivalent linearization", Int. J. Nonlinear Mech., 13(2), 71-78.
10. Tezcan, J. and P.D. Spanos (2006), "A numerical approach for nonlinear system response spectrum determination via wavelets", Proceedings of the 5th International Conference on Computational Stochastic Mechanics, Rodos, Greece, Mill-Press International.
11. Urabe, M. and A. Reiter (1964). Numerical Computation of Nonlinear Forced Oscillations by Galerkin's Procedure. Mathematics Research Center, University of Wisconsin.