ANALYSIS OF GLOBAL SUBHARMONIC ORBITS OF A VIBRO-IMPACT QUASI-HAMILTONIAN SYSTEM WITH THE MELNIKOV'S METHOD

摘要

A global subharmonic Melnikov function (Type III) of a vibro-impact quasi-Hamiltonian system is derived. The function can be applied to determine the existence of global subharmonic motions. This function, together with the homoclinic and the local subharmonic ones (Type I & Type II), reveals lots of local/global features of the quasi-Hamiltonian system. The global subharmonic Melnikov function is validated by numerical simulations of a forced vibro-impact oscillator. Coexistence of multi-solutions is also found in some narrow parametric regions just above the critical lines determined by Melnikov functions.