PurposeThis　paper　explores　the　vibration　control　performance　of　a　combined　vibration　isolation　(CVI)　system,　which　integrates　a　quasi-zero　stiffness　(QZS)　system　with　a　bistable　nonlinear　energy　sink　(BNES).MethodsThe　dynamic　equations　of　the　CVI　system　are　first　established,　and　the　stability　of　the　BNES　equilibrium　point　is　analyzed.　Using　the　harmonic　balance　method　coupled　with　the　arc-length　continuation　method,　the　amplitude-frequency　response　and　force　transmissibility　of　the　system　are　derived,　and　these　analytical　results　are　validated　through　numerical　simulations.ResultsThe　effectiveness　of　the　CVI　system＇s　vibration　control　is　then　assessed　in　terms　of　vibration　amplitude,　force　transmissibility,　and　energy　dissipation.　Finally,　the　impacts　of　parameters　such　as　stiffness,　damping,　mass　ratio,　and　external　excitation　amplitude　on　the　system＇s　vibration　control　performance　are　analyzed　and　compared　with　those　of　a　conventional　CVI　system　coupled　with　NES.ConclusionThe　findings　reveal　that　the　proposed　CVI　system　with　BNES　can　significantly　reduce　peak　amplitudes　and　broaden　the　vibration　isolation　frequency　range.　This　system＇s　mechanism　provides　a　valuable　reference　for　enhancing　the　vibration　control　capabilities　of　QZS　systems.