The　effects　of　nonlinear　energy　sink　(NES)　on　vibration　suppression　of　a　simply　supported　beam　are　investigated　in　this　work.　The　slow　flow　equations　of　the　system　are　derived　by　using　complexification-averaging　method,　and　the　validity　of　the　derivation　is　verified.　By　comparing　the　vibration　absorption　of　single　and　parallel　NESs　of　equal　mass,　it　is　found　that　the　latter　exhibits　superior　vibration　absorption　performance.　In　addition,　the　parallel　NES　can　eliminate　higher　branch　responses　of　the　system　under　the　harmonic　load.　Furthermore,　it　is　found　that　parallel　NES　can　eliminate　the　higher　branches　of　the　system　more　effectively　by　tuning　nonlinear　stiffness　and　damping.　Moreover,　the　thermal　effect　on　natural　frequencies　of　the　simply　supported　beam　is　considered,　and　the　influences　of　the　parallel　NES＇s　parameters　on　the　energy　dissipation　rate　under　shock　load　are　investigated.　The　nonlinear　responses　of　the　simply　supported　beam　with　parallel　NES　under　harmonic　load　and　with　the　increase　of　temperature　are　described.