Using　high-performance　lightweight　functionally　graded　graphene-platelet　reinforced　(FG-GPLR)　porous　composite　plates　opens　up　an　avenue　for　a　new　generation　of　structural　and　material　designs,　which　could　be　tailored　to　the　need　of　specific　applications.　Consider　the　von　Karman　plate　model　with　geometrical　nonlinearity,　the　equation　of　motion　can　be　formulated.　The　Halpin　-　Tsai　model　is　employed　to　predict　the　elastic　properties　of　FG-GPLR　porous　composite　plates.　The　moving　Kriging　interpolation　mesh-free　computational　framework,　which　is　confirmed　to　have　high　computing　performance　in　terms　of　accuracy,　convergence　and　robustness,　is　used　to　discretize　the　nonlinear　vibration　equation.　Then,　the　linearized　updated　mode　(LUM)　method　is　used　to　obtain　iterative　solutions.　An　intensive　work,　investigating　the　influence　of　boundary　constraints,　porosity　distributions,　graphene　platelets　(GPLs),　and　vibration　amplitudes,　is　conducted.　It　is　found　that　a　continuous　increase　in　the　amplitude　parameter　ultimately　yields　an　abrupt　change　of　the　fundamental　frequency,　inducing　a　bistable　vibration　mode　jump　phenomenon.　The　present　results　can　provide　useful　guidelines　for　the　application　design　of　nano-reinforced　composite　structures.