In　high　dimension,　the　bifurcation　theory　of　periodic　orbits　of　nonlinear　dynamics　systems　are　difficult　to　establish　in　general.　In　this　paper,　by　performing　the　curvilinear　coordinate　frame　and　constructing　a　Poincare　map,　we　obtain　some　sufficient　conditions　of　the　bifurcation　of　periodic　solutions　of　some　2n-dimensional　systems　for　the　unperturbed　system　in　two　cases:　one　is　a　decoupled　n-degree-of-freedom　nonlinear　Hamiltonian　system　and　the　other　has　an　isolated　invariant　torus.　We　use　a　new　method　and　study　new　types　of　systems　compared　with　the　existing　results.　As　an　application　we　study　the　bifurcation　and　number　of　periodic　solutions　of　an　ice　covered　suspension　system.　Under　a　certain　parametrical　condition,　the　number　of　periodic　solutions　of　this　system　can　be　2　or　1　with　the　variation　of　parameter　p(2).