In　this　paper,　we　focus　on　the　multiple　periodic　vibration　behaviors　of　an　auxetic　honeycomb　sandwich　plate　subjected　to　in-plane　and　transverse　excitations.　Nonlinear　equation　of　motion　for　the　plate　is　derived　based　on　the　third-order　shear　deformation　theory　and　von　Karman　type　nonlinear　geometric　assumptions.　The　Melnikov　method　is　extended　to　detect　the　bifurcation　and　multiple　periodic　vibrations　of　the　plate　under　1:2　internal　resonance.　The　effects　of　transverse　excitation　on　nonlinear　vibration　behaviors　are　discussed　in　detail.　Evolution　laws　and　waveforms　of　multiple　periodic　vibrations　are　obtained　to　analyze　the　energy　transfer　process　between　the　first　two　order　modes.　Even　quite　small　transverse　excitation　can　cause　periodic　vibration　in　the　system,　and　there　can　be　at　most　three　periodic　orbits　in　certain　bifurcation　regions.　The　periodic　orbits　are　classified　into　two　families　by　tracing　their　sources.　The　study　provides　the　possibility　for　the　classification　study　on　generation　mechanism　of　system　complexity　and　energy　transfers　between　different　modes.