In　this　paper,　a　unified　solution　is　proposed　to　investigate　the　vibration　characteristics　of　the　variable-walled　thickness　graphene-reinforced　porous　aluminum-based　(GRPA)　sandwich　joined　conical-conical　panel　(JCCP)　with　the　arbitrary　elastic　support　boundary　conditions　by　using　the　differential　quadrature　method　(DQM).　The　two　surfaces　of　the　sandwich　JCCP　are　made　of　metallic　aluminum　and　the　central　core　layer　is　the　GRPA.　The　core　thickness　of　each　conical　plate　varies　linearly　with　its　generatrix.　Three　types　of　the　graphene　distributions　and　two　types　of　porosity　distributions　are　considered　along　the　core　thickness　direction.　Based　on　the　first-order　shear　deformation　theory　(FSDT),　von-Karman　strain　displacement　relationship,　constitutive　relationship　and　Hamiltonian　principle,　the　partial　differential　governing　equations　of　motion　are　obtained　for　the　variable　wall　thickness　GRPA　sandwich　JCCP.　Using　the　DQM,　the　dynamic　equation　is　discretized　into　the　ordinary　differential　equation.　The　matrix　of　the　characteristic　equation　is　analyzed　to　solve　the　frequencies　and　mode　shapes　of　the　variable　wall　thickness　GRPA　sandwich　JCCP.　The　effects　of　the　spring　stiffness,　boundary　conditions,　graphene　distributions,　porosity　distributions　and　geometric　parameters　on　the　vibration　properties　are　studied　for　the　variable　wall　thickness　GRPA　sandwich　JCCP　with　two　interesting　elastic　supported　boundary　conditions.　At　the　same　time,　this　article　provides　a　useful　approach　for　studying　the　arbitrary　boundary　coupled　plate　and　shell　structures　with　the　variable　wall　thickness.