A　general　modeling　approach　is　presented　to　analyze　the　free　vibration　behavior　of　the　spatially　coupled　shell-plate　system　(SCSPS)　with　complex　geometric　shapes.　The　coupling　mechanism　established　by　the　penalty　function　method　can　be　applied　not　only　to　the　SCSPS　but　also　to　other　extensively　studied　shell-plate　structures.　The　conventional　method　for　irregularly-shaped　plates　involves　the　utilization　of　one-to-one　mapping　technology　(OTOMT)　to　transform　the　two-dimensional　plane　domain　of　the　plate　into　a　square　domain,　aiming　to　fulfill　the　numerical　solution　requirement　for　integral　calculation.　However,　since　the　OTOMT　is　a　planar　mapping　technique　that　cannot　be　applied　to　shells,　in　this　paper,　we　propose　a　coordinate　transformation　strategy　to　convert　two-dimensional　shells　into　plane　geometry　in　order　to　address　this　limitation.　The　vibration　problem　is　simultaneously　resolved　numerically　using　the　Hamilton＇s　principle　and　the　Jacobi　spectral　method.　The　current　method　is　validated　for　several　key　capabilities　based　on　three　case　studies,　as　well　as　modal　experiments　and　the　commercial　finite　element　software.　Additionally,　a　series　of　model　evaluations　are　employed　to　demonstrate　the　advantages　of　the　current　method.　Moreover,　the　results　of　the　parametric　study　illustrate　the　impact　of　several　variables　on　the　natural　frequency　of　the　structure.　©　2024　Elsevier　Ltd