TY - JOUR
T1 - A perturbation-incremental method for the calculation of semi-stable limit cycles of strongly non-linear oscillators
AU - Chen, S. H.
AU - Chan, J. K H
AU - Leung, A. Y T
PY - 2000
Y1 - 2000
N2 - The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form ẍ + g(x) = λf(x, ẋ, μ)ẋ is studied by the perturbation-incremental method. Firstly, the ordinary differential equation is transformed into an integral equation by a non-linear time transformation, then the initial solution for λ ≈ 0 is obtained by using the perturbation method. Secondly, the solution for an arbitrary value of λ can be determined by using the incremental approach. Two examples are given to show the efficiency and accuracy of the present method. Copyright © 2000 John Wiley & Sons, Ltd.
AB - The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form ẍ + g(x) = λf(x, ẋ, μ)ẋ is studied by the perturbation-incremental method. Firstly, the ordinary differential equation is transformed into an integral equation by a non-linear time transformation, then the initial solution for λ ≈ 0 is obtained by using the perturbation method. Secondly, the solution for an arbitrary value of λ can be determined by using the incremental approach. Two examples are given to show the efficiency and accuracy of the present method. Copyright © 2000 John Wiley & Sons, Ltd.
KW - Perturbation-incremental method
KW - Semi-stable limit cycles
KW - Strongly non-linear oscillators
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M3 - RGC 22 - Publication in policy or professional journal
VL - 16
SP - 301
EP - 313
JO - Communications in Numerical Methods in Engineering
JF - Communications in Numerical Methods in Engineering
SN - 1069-8299
IS - 5
ER -