The dynamics of a beam continuously joined to an elastic substrate, such a system which arises in geotechnics, in structural mechanics and in many other branches of engineering, have received considerable attention.This model proposed by Winkler[1].presents abundant dynamical behaviors and still preserves practical and theoretical relevance.Refer to.for example.P.L.Pasterna[2].S.Lenci and A.M.Tarantino[3].Two classes of global bifurcations near the critical load for this system have been detected analytically using the Metnikov method[4].