In　this　paper,　the　natural　vibration　of　an　elastically　supported　porous　truncated　joined　conical-conical　shell　(JCCS)　is　studied.　The　elastic　support　is　achieved　by　using　artificial　spring　technology.　Four　types　of　the　metal　foam　porous　distribution　are　presented,　i.e.　the　uniform　distribution　along　the　radial　direction　and　three　other　types　of　the　gradient　distribution.　By　applying　Hamilton　principle　and　the　first　order　shear　deformation　theory　(FSDT),　dynamic　equations　of　motion　of　the　JCCS　in　the　form　of　partial　differential　are　derived.　Considering　the　elastically　supported　boundary　conditions,　displacements　continuity　conditions　and　forces　continuity　conditions　at　the　joining　section　of　the　coupling　conical　shell,　partial　differential　equations　used　to　describe　this　dynamic　system　are　simplified　into　a　set　of　algebraic　equations　by　utilizing　the　generalized　differential　quadrature　method　(GDQM),　in　which　the　trigonometric　function　is　used　in　the　circumferential　direction,　while　in　meridian　direction　the　DQ　is　applied.　To　obtain　the　natural　vibration　characteristic　of　the　JCCS,　the　eigenvalue　solving　technology　is　utilized.　The　validation　and　convergence　of　the　theoretical　formulation　are　confirmed　by　comparison　studies.　Influences　of　boundary　conditions,　the　spring　stiffness,　the　geometric　and　material　parameters　on　natural　frequencies　and　mode　shapes　of　the　JCCS　with　two　particular　elastic　boundary　conditions　are　studied　in　detail.(c)　2022　Elsevier　Masson　SAS.　All　rights　reserved.