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.

建立了一种在周期激励下具有双向刚性约束的双稳态冲击振荡器，并通过扩展解析梅尔尼科夫方法对非光滑系统和动力学实验分别进行了详细的全局动力学研究。首先，从几何学的新观点出发，将梅尔尼科夫方法扩展为抽象的非光滑动力系统，该系统表示一类具有双边刚性约束的双稳态冲击振荡器。其次，难以获得单斜轨道的解析表达式，采用半解析半数值方法计算梅尔尼科夫函数，以求得已建立的冲击振荡器的整体分叉和混沌振荡的参数阈值。然后，