Melnikov's method for a general nonlinear vibro-impact oscillator

Wei Xu; Jinqian Feng; Haiwu Rong

doi:10.1016/j.na.2008.10.120

Melnikov's method for a general nonlinear vibro-impact oscillator

Wei Xu
, Jinqian Feng
, Haiwu Rong

School of Mathematics and Statistics

Northwestern Polytechnical University Xian
Foshan University

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

Melnikov's method is presented for a general nonlinear vibro-impact oscillator, and Melnikov function for homoclinic orbits is obtained analytically. A Duffing vibro-impact oscillator is given to illustrate the application of the procedures. The obtained results are verified by the phase portrait, Poincaré surface of section and bifurcation diagrams.

Original language	English
Pages (from-to)	418-426
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	1-2
DOIs	https://doi.org/10.1016/j.na.2008.10.120
State	Published - 1 Jul 2009

Keywords

Homoclinic orbit
Melnikov's method
Non-smooth system
Vibro-impact oscillator

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10.1016/j.na.2008.10.120

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title = "Melnikov's method for a general nonlinear vibro-impact oscillator",

abstract = "Melnikov's method is presented for a general nonlinear vibro-impact oscillator, and Melnikov function for homoclinic orbits is obtained analytically. A Duffing vibro-impact oscillator is given to illustrate the application of the procedures. The obtained results are verified by the phase portrait, Poincar{\'e} surface of section and bifurcation diagrams.",

keywords = "Homoclinic orbit, Melnikov's method, Non-smooth system, Vibro-impact oscillator",

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AU - Xu, Wei

AU - Feng, Jinqian

AU - Rong, Haiwu

PY - 2009/7/1

Y1 - 2009/7/1

N2 - Melnikov's method is presented for a general nonlinear vibro-impact oscillator, and Melnikov function for homoclinic orbits is obtained analytically. A Duffing vibro-impact oscillator is given to illustrate the application of the procedures. The obtained results are verified by the phase portrait, Poincaré surface of section and bifurcation diagrams.

AB - Melnikov's method is presented for a general nonlinear vibro-impact oscillator, and Melnikov function for homoclinic orbits is obtained analytically. A Duffing vibro-impact oscillator is given to illustrate the application of the procedures. The obtained results are verified by the phase portrait, Poincaré surface of section and bifurcation diagrams.

KW - Homoclinic orbit

KW - Melnikov's method

KW - Non-smooth system

KW - Vibro-impact oscillator

UR - https://www.scopus.com/pages/publications/64849095397

U2 - 10.1016/j.na.2008.10.120

DO - 10.1016/j.na.2008.10.120

M3 - 文章

AN - SCOPUS:64849095397

SN - 0362-546X

VL - 71

SP - 418

EP - 426

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1-2

ER -

Melnikov's method for a general nonlinear vibro-impact oscillator

Abstract

Keywords

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