Damage　can　be　identified　using　generalized　flexibility　matrix　based　methods,　by　using　the　first　natural　frequency　and　the　corresponding　mode　shape.　However,　the　first　mode　is　not　always　appropriate　to　be　used　in　damage　detection.　The　contact　interface　of　rod-fastened-rotor　may　be　partially　separated　under　bending　moment　which　decreases　the　flexural　stiffness　of　the　rotor.　The　bending　moment　on　the　interface　varies　as　rotating　speed　changes,　so　that　the　first-　and　second-modal　parameters　obtained　are　corresponding　to　different　damage　scenarios.　In　this　paper,　a　structural　damage　detection　method　requiring　single　nonfirst　mode　is　proposed.　Firstly,　the　system　is　updated　via　restricting　the　first　few　mode　shapes.　The　mass　matrix,　stiffness　matrix,　and　modal　parameters　of　the　updated　system　are　derived.　Then,　the　generalized　flexibility　matrix　of　the　updated　system　is　obtained,　and　its　changes　and　sensitivity　to　damage　are　derived.　The　changes　and　sensitivity　are　used　to　calculate　the　location　and　severity　of　damage.　Finally,　this　method　is　tested　through　numerical　means　on　a　cantilever　beam　and　a　rod-fastened-rotor　with　different　damage　scenarios　when　only　the　second　mode　is　available.　The　results　indicate　that　the　proposed　method　can　effectively　identify　single,　double,　and　multiple　damage　using　single　nonfirst　mode.