Based　on　a　rigid-flexible　piezoelectric　energy　harvester　(PEH)　composed　of　antisymmetric　double　plates　with　a　rigid　frame,　which　has　three　operating　bandwidths　in　a　low-frequency　range,　nonlinearity　is　used　to　further　broaden　the　operating　bandwidth.　Firstly,　finite-element　simulation　is　used　to　study　the　influence　of　structural　parameters,　such　as　the　width　of　the　frame　and　the　distance　between　two　plates,　on　the　natural　frequencies.　Bending　deformation　of　cantilever　plates　and　rigid　motion　of　frame　are　considered　comprehensively　to　obtain　the　theoretical　mode　functions　of　the　structure.　The　nonlinear　electromechanical　coupling　model　is　established　via　von　Karman　nonlinear　geometric　assumptions　and　the　Hamilton　principle.　In　order　to　study　the　broadening　of　output　bandwidth　caused　by　nonlinearity,　the　average　equations　with　1:1.5:2　internal　resonance　ratio　are　derived　by　the　multi-scale　method.　On　the　basis　of　the　calculated　optimal　resistance,　the　voltage　response　and　dimensionless　amplitude　response　curves　induced　by　the　first　three　order　modes　are　numerically　calculated.　Theoretical　analysis　shows　that　the　proposed　PEH　not　only　obtains　three　peaks　of　voltage　output　in　a　low-frequency　range,　but　also　utilizes　hard　spring　effect　and　internal　resonance　to　widen　the　output　bandwidth　of　each　resonance　interval.　Copyright　(C)　2021　EPLA