Open AccessEscape time from potential wells of strongly nonlinear oscillatorswith slowly varying parameters
Author(s) -
Jianping Cai,
Y. P. Li,
Xiaofeng Wu
Publication year - 2005
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/mpe.2005.365
Subject(s) - jacobian matrix and determinant , elliptic function , nonlinear system , oscillation (cell signaling) , mathematics , mathematical analysis , taylor series , series (stratigraphy) , elliptic integral , function (biology) , quadratic equation , asymptotic expansion , character (mathematics) , amplitude , physics , geometry , quantum mechanics , paleontology , evolutionary biology , biology , genetics
The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well ofquadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function.Numerical examples verify the efficiency of the present method
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