Parametrically excited system studied by dynamic branch switching method

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 (FFT). All singularities, folds, flips, period doubling and predicted 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 are discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted.