Abstract
A new bistable impact oscillator with bilateral rigid constraints under periodic excitations is established and the global dynamics are studied in detail respectively by the extended analytical Melnikov method for non-smooth systems and dynamical experiments. Firstly, the Melnikov method is extended from a new viewpoint of geometry for an abstract non-smooth dynamical system denoting a class of bistable impact oscillators with bilateral rigid constraints. Secondly, the analytical expression of homoclinic orbits is difficult to obtain, a semi-analytical and semi-numerical method for calculating the Melnikov function is applied to obtain the threshold of parameters for the global bifurcations and chaotic oscillations of the established impact oscillator. Then, numerical simulations and dynamical experiments are carried out together to show intra-well periodic oscillations, inter-well periodic or chaotic oscillations under different amplitudes of periodic excitations, which furthermore validates the reliability of the extended Melnikov method for this class of non-smooth systems.
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