A dynamic branch-switching method for parametrically excited systems

A.Y.T. Leung; T. Ge

doi:10.1155/1999/584719

A dynamic branch-switching method for parametrically excited systems

A.Y.T. Leung^*, T. Ge

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational) nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM). All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted. © 1999, IOS Press. All rights reserved.

Original language	English
Article number	584719
Pages (from-to)	183-196
Journal	Shock and Vibration
Volume	6
DOIs	https://doi.org/10.1155/1999/584719
Publication status	Published - 1999
Externally published	Yes

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title = "A dynamic branch-switching method for parametrically excited systems",

abstract = "The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational) nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM). All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted. {\textcopyright} 1999, IOS Press. All rights reserved.",

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year = "1999",

doi = "10.1155/1999/584719",

language = "English",

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pages = "183--196",

journal = "Shock and Vibration",

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TY - JOUR

T1 - A dynamic branch-switching method for parametrically excited systems

AU - Leung, A.Y.T.

AU - Ge, T.

PY - 1999

Y1 - 1999

N2 - The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational) nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM). All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted. © 1999, IOS Press. All rights reserved.

AB - The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational) nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM). All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted. © 1999, IOS Press. All rights reserved.

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U2 - 10.1155/1999/584719

DO - 10.1155/1999/584719

M3 - RGC 21 - Publication in refereed journal

SN - 1070-9622

VL - 6

SP - 183

EP - 196

JO - Shock and Vibration

JF - Shock and Vibration

M1 - 584719

ER -

A dynamic branch-switching method for parametrically excited systems

Abstract

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