The　metamaterial　with　negative　Poison＇s　ratio　is　widely　used　due　to　its　special　mechanical　and　physical　properties.　Based　on　the　theory　of　periodic　solution　and　bifurcation　of　nonlinear　dynamics,　we　mainly　focus　on　the　nonlinear　vibration　behaviors　and　parameter　control　of　a　simply　supported　concave　hexagonal　composite　sandwich　plate　with　negative　Poisson＇s　ratio　in　auxetic　honeycombs　subjected　to　in-plane　and　transverse　excitation.　The　Melnikov　function　is　improved　by　introducing　the　curvilinear　coordinate　frame　and　Poincaré　map　to　detect　the　existence　and　number　of　the　periodic　solutions.　The　effects　of　the　forcing　excitation　coefficient　on　nonlinear　dynamics　as　well　as　the　parameter　control　conditions　are　presented.　Numerical　method　is　performed　to　obtain　the　phase　portraits　of　the　number　and　corresponding　positions　of　multiple　periodic　orbits.　©　Published　under　licence　by　IOP　Publishing　Ltd.