Melnikov’s method for a general nonlinear vibro-impact oscillator

Melnikov’s method is presented for a general nonlinear vibro-impact oscillator, and Melnikov function for homoclinic orbits is obtained analytically. A Duffing vibro-impact oscillator is given to illustrate the application of the procedures. The obtained results are verified by the phase portrait, Poincaré surface of section and bifurcation diagrams.