Autonomous　systems　with　periodic　solutions　are　frequently　encountered　in　applications.　In　this　paper,　the　Melnikov　function　and　the　theory　of　Poincare　mapping　were　obtained　for　the　existence　of　2　pi-periodic　solution　of　the　sandwich　plate　system　in　1:2　internal　resonances.　Moreover,　some　groups　of　phase　diagrams　under　different　conditions　were　obtained.　This　paper　reveals　the　flutter　and　pneumatic　elastic　properties　of　the　sandwich　plate,　and　it　is　expected　that　the　results　in　this　paper　could　provide　the　theoretical　basis　for　the　design　of　the　composite　materials.