A　swing-arm　type　lightweight　and　flexible　acoustic　metamaterial　is　proposed　to　deal　with　the　problem　of　low-frequency　noise　in　vehicles　that　cannot　be　effectively　attenuated　by　ordinary　acoustic　materials.　Broadening　the　band　of　sound　transmission　loss　(STL)　and　improving　the　STL　amplitude　are　realized　by　introducing　multi-state　anti-resonance　modes　into　subcells.　A　flexible　ethylene　vinyl　acetate　copolymer　(EVA)　material　is　used　as　the　frame　of　the　metamaterial,　and　four　metal　platelets　and　a　cross-like　EVA　swing　arm　are　applied　onto　the　surface　of　polyimide　(PI)　membrane　with　a　thickness　of　0.2　mm　to　create　resonant　parts.　The　broadening　mechanisms　of　STL　bandwidth　are　revealed　through　the　numerical　analyses　of　STL,　multi-state　anti-resonance　modes　and　negative　effective　parameters　of　a　supercell　unit.　A　large-scale　flexible　sound　insulation　metamaterial　is　designed　based　on　the　derivation　of　the　supercell　structure,　and　assembled　into　the　hood　of　an　automobile　engine.　Its　attenuation　ability　to　low-frequency　noise　is　further　estimated　by　the　＇reverberation　chamber-anechoic　chamber＇　sound　insulation　experiment　and　the　real　vehicle　noise　reduction　tests.　Relevant　research　results　show　that　the　multi-state　anti-resonance　synergy　modes　between　the　subcells　modulate　the　supercell　into　a　continuous　dynamic　balance　state,　cause　low-frequency　incident　and　reflected　sound　waves　to　cancel　each　other　out,　and　realize　the　widening　of　the　sound　insulation　bandwidth　and　the　improvement　of　the　sound　insulation　capacity.　The　designed　metamaterial　makes　the　average　noise　attenuation　of　engine　below　1　kHz　up　to　3　dB(A).　The　results　of　this　study　provide　a　new　idea　for　the　design　of　low-frequency　broadband　sound　insulation　materials,　and　have　potential　engineering　application　prospects　in　the　low-frequency　noise　control.　©　2020,　Editorial　Office　of　Journal　of　Xi＇an　Jiaotong　University.　All　right　reserved.