In　this　paper,　a　unified　dynamic　modeling　for　investigating　the　free　and　forced　vibration　of　the　functionally　graded　material　(FGM)　sandwich　conical　shell　built-in　reinforcing　plate　structures　with　arbitrary　curve　coupled　boundaries　is　established.　The　structure　is　split　into　three　structures　by　the　intercept　b　and　slope　k　of　the　relative　position　intersection　curve　which　include　hyperbola,　parabola　etc.　The　subshell　is　FGM　sandwich　shell　and　subjected　to　a　temperature　distribution　field　and　airflow　environment.　Theoretical　model　of　the　substructure　is　expressed　by　using　the　Jacobian　differential　quadrature　method　(JDQM).　Thereinto,　the　governing　equations　are　derived　from　the　Hamilton　principle　based　on　the　first-order　shear　theory.　To　solve　the　coupling　problem　of　curve　boundaries　in　modeling　process,　a　general　penalty　function　is　used　to　describe　it.　On　this　basis,　a　novel　coupling　method　of　spatial　curve　integral　penalty　function　is　developed　by　the　coordinate　transformation　of　the　curve　boundary　displacement　function.　After　comparing　with　the　finite　element　method　(FEM)　results　and　verifying　the　effectiveness　of　the　theoretical　model,　a　series　of　numerical　cases　of　the　effects　of　geometry,　material　distribution,　temperature　field　and　incoming　airflow　velocity　on　the　free　and　forced　vibration　characteristics　are　presented,　which　provides　a　reliable　framework　for　studying　the　dynamic　behavior　of　the　FGM　sandwich　conical　shell　built-in　reinforcing　plate　exposed　in　the　airflow.　In　the　parametric　study,　it　was　observed　that　increasing　the　intercept　b,　while　keeping　the　slope　k　constant,　can　enhance　the　performance　of　the　structure.　©　2025　Elsevier　Masson　SAS