The　double　excitation　multi-stability　and　Shilnikov-type　multi-pulse　jumping　chaotic　vibrations　are　analyzed　for　the　bistable　asymmetric　laminated　composite　square　panel　under　foundation　force　for　the　first　time.　Based　on　the　extended　new　high-dimensional　Melnikov　function,　the　explicit　sufficient　conditions　are　obtained　for　the　existence　of　the　Shilnikov-type　multi-pulse　jumping　homoclinic　orbits　and　chaotic　vibrations　in　the　bistable　asymmetric　laminated　composite　square　panel,　which　implies　that　multi-pulse　jumping　chaotic　vibrations　may　occur　in　the　sense　of　Smale　horseshoes.　The　extended　new　high-dimensional　Melnikov　function　gives　the　parameters　domain　of　the　intersection　for　the　homoclinic　orbits,　which　illustrates　the　relationship　among　the　coefficients　of　damping,　parametric,　and　external　excitations.　Numerical　simulations　including　the　bifurcation　diagrams,　largest　Lyapunov　exponents,　phase　portraits,　waveforms,　and　Poincare　sections　are　utilized　to　study　the　double　excitation　multi-pulse　jumping　and　metastable　chaotic　vibrations　and　dynamic　snap-through　phenomena.　The　numerical　results　demonstrate　that　double　excitation　Shilinikov　multi-pulse　jumping　chaotic　and　small　metastable　chaotic　vibrations　coexist　in　the　bistable　asymmetric　laminated　composite　square　panel.　It　is　found　that　the　external　excitation　changes　the　complexity　of　the　chaos,　while　the　parameter　excitation　changes　the　type　of　chaos.　It　is　verified　that　the　bistable　asymmetric　laminated　composite　square　panel　with　small　damping　is　easier　to　produce　double　excitation　Shilinikov　multi-pulse　jumping　chaotic　vibrations.