A dynamic branch-switching method for parametrically excited systems
Author(s)
Author(s)
Ge, T.
Date Issued
1999
Publisher
Hindawi Publishing Corporation
Journal
Shock and Vibration
Volume
6
Start page
183
End page
196
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.
SFU Affiliated Publication
No
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