This　paper　researches　the　dynamic　snap-through　phenomena　and　the　coexistence　of　the　multi-pulse　jumping　chaotic　dynamics　in　bistable　equilibrium　positions　and　the　large　amplitude　nonlinear　vibrations　for　a　simply　supported　buckled　3D-kagome　truss　core　sandwich　rectangular　plate　under　combined　transverse　and　in-plane　excitations　based　on　the　extended　high-dimensional　Melnikov　method.　According　to　the　two-degree-of-freedom　non-autonomous　nonlinear　dynamical　system　of　the　buckled　truss　core　sandwich　rectangular　plate　and　the　theory　of　normal　form,　it　is　found　that　some　nonlinear　terms　have　less　effects　on　the　nonlinear　dynamic　responses　than　other　nonlinear　terms.　The　extended　high-dimensional　Melnikov　method　is　employed　to　investigate　the　dynamic　snap-through　phenomena　and　the　bistable　multi-pulse　jumping　chaotic　vibrations　around　the　upper-mode　and　the　lower-mode　for　two　different　cases　of　buckling　in　the　truss　core　sandwich　rectangular　plate.　A　numerical　method　is　used　to　detect　the　bistable　multi-pulse　jumping　chaotic　vibrations　around　two　stable　equilibrium　positions　for　the　non-autonomous　buckled　truss　core　sandwich　rectangular　plate.　The　obtained　theoretical　and　numerical　results　indicate　that　there　exists　the　coexistence　of　the　bistable　multi-pulse　jumping　chaotic　vibrations　and　the　large　amplitude　nonlinear　vibrations　in　the　buckled　truss　core　sandwich　rectangular　plate　under　combined　transverse　and　in-plane　excitations.