A　dynamic　model　built　theoretically　and　simulated　numerically　for　an　unsymmetric　bistable　laminate　is　elucidated,　elaborating　the　dynamic　regimes.　Peak-to-peak　amplitude　diagrams　being　amplitude-frequency　and　amplitude-force　response　curves　are　derived.　The　single-well　vibrations,　the　limit-cycle　oscillations,　the　multiple-period　dynamic　snap-through,　the　chaotic　dynamic　snap-through　and　the　intermittency　dynamic　snap-through　can　be　detected.　The　amplitude-frequency　response　curves　exhibit　the　softening　stiffness　effect.　The　dynamic　regimes　are　correlated　with　the　excitation　amplitude　and　the　modal　frequencies.　Deploying　the　high-level　excitation　amplitude　and　the　low-level　modal　frequency　leads　to　the　limit-cycle　oscillations.　Besides,　the　single-well　vibrations　are　characterized　by　the　period-doubling　bifurcation.