The　band　gap　characteristics　of　periodic　structures　provide　a　new　idea　for　the　field　of　seismic　isolation　in　civil　engineering，among　which　the　one-dimensional　periodic　foundation　structure　has　garnered　significant　attention　due　to　its　simple　structure　and　economical　applicability.　In　this　paper，by　studying　the　vibration　characteristics　of　the　one-dimensional　periodic　base　structure，an　approximate　analytical　solution　for　calculating　the　one-dimensional　rubber-concrete　periodic　base　band　gap　is　derived，and　on　this　basis，a　one-dimensional　rubber-concrete　periodic　foundation　optimization　design　method　based　on　the　resonance　zone　of　the　superstructure　is　proposed.　Numerical　examples　in　the　frequency　domain　and　time　domain　show　that　the　periodic　foundation　designed　by　this　optimization　method　can　ensure　a　good　damping　effect　of　its　superstructure　in　a　wide　and　continuous　frequency　range.　©　2024　Nanjing　University　of　Aeronautics　an　Astronautics.　All　rights　reserved.