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Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation
Xiujing Han1, Qinsheng Bi1, Peng Ji2,3
1Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang Jiangsu 212013, People's Republic of China.
Abstract:
We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary m:n relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.
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