In　order　to　conduct　research　on　the　bifurcations　of　multiple　limit　cycles　for　a　parametrically　and　externally　excited　mechanical　system,　the　vector　field　of　the　averaged　equations　in　the　form　of　a　perturbed　polynomial　Hamiltonian　system　of　degree　7　through　perturbed　analysis　was　established.　By　using　the　bifurcation　theory　of　planar　dynamical　system　and　the　Maple　symbolic　computation　program,　we　controlled　the　parameters　to　obtain　40　limit　cycles　under　one　group　of　control　conditions　and　the　configurations　of　compound　eyes　were　also　obtained.　This　result　may　serve　as　theoretical　reference　for　the　control　problem　of　a　parametrically　and　externally　excited　mechanical　system.