Folded　beam　structures　have　been　widely　used　in　mechanical　engineering,　aerospace　engineering,　and　other　fields　due　to　their　flexibility　and　extensibility　in　applications.　Although　the　components　of　a　folded　beam　are　simple　beam　structures,　building　an　accurate　dynamic　model　is　complex　due　to　its　multi-degree-of-freedom,　multi-mode,　and　close-mode　features.　This　study　presents　a　novel　method　to　analyze　in-plane　free　vibration　of　a　multi-folded　beam　structure　with　arbitrary　numbers　of　beam　segments　with　different　beam　lengths　and　folding　angles.　The　governing　equations　of　the　system　can　be　easily　obtained　based　on　the　beam　theory　and　the　work-energy　principle.　However,　the　key　issue　is　how　to　solve　the　eigenvalue　problem　of　a　multi　degree　of　freedom　system　defined　by　a　6　n　×　6　n　matrix.　As　the　coefficient　solution　vector　of　the　modal　function　is　unknown,　solving　equations　defined　by　high-order　determinants　involving　variables　has　considerable　complexity.　In　this　work,　the　intricate　matrix　is　initially　turned　into　a　single　matrix　of　block　Hessenberg　form　using　numerous　“6　×　6”　block　square　matrices.　Furthermore,　by　combining　the　characteristics　of　the　block　Hessenberg　matrix　with　the　approach　to　solve　block　determinants,　a　considerable　reduction　in　the　determinant＇s　size　can　be　attained,　diminishing　it　from　a　dimension　of　6　n　×　6　n　to　6　×　6.　This　procedure　markedly　simplifies　the　computational　intricacies　involved　in　the　analysis.　Finally,　four　kinds　of　multi-folded　beams,　namely　L-shaped　beams,　Z-shaped　beams,　C-shaped　beams,　and　four-segment　folded　beams　with　arbitrary　lengths,　folding　angles,　and　numbers　of　beam　segments　are　considered　and　studied,　and　the　mode　shapes　and　the　influence　of　geometric　parameters　on　the　first　three　natural　frequencies　are　discussed　in　detail.　The　results　are　also　verified　by　the　finite　element　method　(FEM),　and　good　agreement　is　found　between　the　two　methods.　The　results　show　that　the　proposed　method　can　offer　a　unified　framework　for　the　in-plane　vibration　analysis　of　multi-folded　beam　structures.　©　2024　Elsevier　Ltd