A dynamic branch‐switching method for parametrically excited systems

Article type: Research Article

Authors: Leung, A.Y.T.^; | Ge, T.

Affiliations: School of Engineering, University of Manchester, Manchester M13 9PL, UK

Note: [] Corresponding author. From 1 September 1999 for two years on leave to: Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Hong Kong. E‐mail: andrew.leung@cityu.edu.hk.

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.

Journal: Shock and Vibration, vol. 6, no. 4, pp. 183-196, 1999