Linear　and　nonlinear　vibration　characteristics　of　the　graphene　platelet-reinforced　composite　(GPLRC)　laminated　plates　are　investigated.　Based　on　the　first-order　shear　theory　and　von　Karman　geometric　nonlinearity,　the　energy　expressions　of　the　GPLRC　laminates　are　established.　The　boundary　elastic　potential　energy　is　established　by　penalty　function　method　to　simulate　different　boundary　conditions.　The　linear　and　nonlinear　frequencies　of　the　GPLRC　laminated　plate　are　calculated　by　introducing　boundary　potential　energy　into　Rayleigh–Ritz　method.　The　convergence　and　accuracy　of　the　method　are　verified　by　numerical　examples,　and　the　effects　of　different　parameters　on　frequency　are　analyzed.　Considering　the　cantilever　boundary　conditions,　the　nonlinear　motion　governing　equations　of　the　GPLRC　laminated　plate　are　obtained　by　Hamilton　principle.　The　two-degree-freedom　ordinary　differential　motion　equations　of　the　laminates　are　derived　by　Galerkin　method.　Considering　the　fundamental　parameter　resonance　and　1:1　internal　resonance,　the　amplitude–frequency　response　curves　of　the　structure　under　transverse　excitation　are　obtained.　The　effects　of　transverse　excitation　and　damping　coefficient　on　nonlinear　vibration　characteristics　of　the　GPLRC　laminated　plates　are　investigated　by　numerical　simulation.　©　2023　Elsevier　Ltd