A　semi-analytical　method　and　related　experiments　are　present　in　this　paper　to　investigate　the　free　vibration　characteristics　of　the　closed-coupled　plates　with　arbitrary　spatial　coupling　angles　and　curved　edges,　which　are　the　widely　used　structural　form　but　researched　for　the　first　time.　By　combining　the　penalty　function　method　with　flexible　setting　virtual　spring　stiffness　functions　and　the　comprehensive　relative　motion　relation　matrices　along　the　edges　of　the　plates　system,　various　types　of　boundary　and　spatial　coupling　connection　conditions　in　practical　engineering　can　be　constructed.　The　semi-analytical　solution　formulas　for　the　entire　vibration　model　are　established　by　using　the　first-order　shear　deformation　theory　(FSDT)　and　the　two-dimensional　Jacobian　differential　quadrature　method　(JDQM).　To　fulfill　the　requirements　of　integral　operations　for　displacement　approximation　functions,　the　irregular　domain　mapping　technique　is　employed　to　transform　the　irregular　solving　domain　into　the　regular　basic　domain.　The　accuracy　and　applicability　of　the　present　method　in　predicting　eigenfrequencies　and　mode　shapes　are　proved　by　hammer　modal　tests　concerning　four　pyramid/frustum-like　built-up　plates,　comparisons　with　results　from　the　open　literature,　as　well　as　the　finite　element　method　(FEM)　simulations　of　several　specially　designed　cases.　Moreover,　many　meaningful　conclusions　are　drawn　regarding　the　effects　of　spatial　geometric　parameters　on　the　free　vibration　characteristics　of　spatially　closed-coupled　plates　with　curved　edges.　©　2023　Elsevier　Ltd