In　this　paper,　we　introduce　a　curvilinear　coordinate　transformation　to　study　the　bifurcation　of　periodic　solutions　from　a　2-degree-of-freedom　Hamiltonian　system,　when　it　is　perturbed　in　Rm+4　,　where　m　represents　any　positive　integer.　The　extended　Melnikov　function　is　obtained　by　constructing　a　Poincar　&　eacute;　map　on　the　curvilinear　coordinate　frame　of　the　trajectory　of　the　unperturbed　system.　Then　the　criteria　for　bifurcation　of　periodic　solutions　of　these　Hamiltonian　systems　under　isochronous　and　non-isochronous　conditions　are　obtained.　As　for　its　application,　we　study　the　number　of　periodic　solutions　of　a　composite　piezoelectric　cantilever　rectangular　plate　system　whose　averaged　equation　can　be　transformed　into　a　(2+4)-dimensional　dynamical　system.　Furthermore,　under　the　two　resonance　conditions　of　1:1　and　1:2,　we　obtain　the　periodic　solution　numbers　of　this　system　with　the　variation　of　para-metric　excitation　coefficient　p(1).