Engine　blades　are　generally　installed　on　disks　via　dovetail　joints,　which　can　alleviate　stress　concentrations　at　the　blade　root　and　prevent　heat　transfer.　As　a　result,　the　connection　stiffness　is　strongly　affected　by　the　clearance　between　the　blade　and　disk　as　well　as　the　rotation　speed　of　the　blade.　This　paper　first　proposes　a　functionally　graded　graphene-reinforced　titanium　alloy　trapezoid　plate　with　elastic　boundary　conditions　to　investigate　the　large　amplitude　vibration　of　rotating　dovetailed　blades.　The　elastic　boundaries　are　modelled　by　applying　a　series　of　artificial　springs,　and　the　related　admissible　displacement　functions　are　constructed　by　orthogonal　polynomials　through　the　Gram-Schmidt　process.　The　governing　equations　of　the　functionally　graded　graphene　platelet　reinforced　composite　(FG-GPLRC)　trapezoid　plate　are　derived　by　the　first-order　shear　deformation　theory　(FSDT)　and　Lagrange　equation.　The　numerical　results　of　the　large　amplitude　vibration　of　the　plate　are　obtained　by　the　weighted　residual　method　combined　with　a　direct　iterative　algorithm　and　verified　through　analytical　solutions　of　the　harmonic　balance　method.　The　effects　of　the　stiffness　of　the　constraint　springs,　rotation　speed　and　structural　parameters　on　the　linear　and　nonlinear　free　vibrations　of　the　FG-GPLRC　trapezoid　plate　are　thoroughly　studied.