Nonlinear vibratory interactions between a linear and a non-smooth forced oscillator in the gravitational field

Nonlinear interactions of two coupled forced oscillators in the gravitational field are studied. The first oscillator that is supposed to be linear is coupled to a system which possesses multi-phase non-smooth non-conservative and restoring forces. The mass ratio of two oscillators is very small. Studying the system at fast time scale reveals an invariant manifold which depends on the amplitude of applied force on the non-smooth oscillator while slow dynamics of the system around its invariant demonstrates its equilibrium and singular points. Detected time multi-scale dynamics of the system can be endowed for designing proper controller and/or harvester non-smooth oscillators which presents final desirable periodic and/or strongly modulated responses.