A dynamic branch-switching method for parametrically excited systems

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 mu ltiple frequency components. The frequency components of the (irrational) n onlinearity of oscillator are obtained by Fast Fourier Transform and Toepli tz Jacobian method (FFT/TJM). All singularities, folds, Rips, period doubti ng and period bubbling, are computed accurately in an analytical manner. Co existing solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains i s discussed. A highly nonlinear parametrically excited system is given as e xample. All connected solution paths are predicted.