The　flip-flow　vibrating　screen　(FFVS)　is　a　novel　multi-body　screening　equipment　that　utilizes　vibrations　to　classify　bulk　materials　in　the　field　of　screening　machinery.　The　relative　amplitude　of　FFVSs　determines　the　tension　and　ejection　intensity　of　elastic　flip-flow　screen　panels,　which　is　a　critical　operating　parameter　affecting　the　screening　performance.　However,　FFVSs　generally　suffer　from　large　variations　of　relative　amplitude　caused　by　the　loading　of　materials　and　the　changes　in　shear　spring　stiffness　(the　temperature　changes　of　the　shear　springs　lead　to　their　stiffness　changes),　which　significantly　reduce　the　screening　efficiency　and　lifespan　of　FFVSs.　To　address　this　problem,　this　paper　proposes　a　nonlinear　stiffness-based　method　for　stabilizing　the　vibration　amplitude　of　FFVSs　using　piecewise　linear　springs.　By　introducing　these　springs　between　the　two　frames,　the　sensitivity　of　the　relative　amplitude　to　shear　spring　stiffness　is　reduced,　thereby　achieving　the　stabilization　of　the　relative　amplitude　of　FFVSs.　In　this　study,　the　variations　of　the　vibration　amplitude　of　the　FFVS　due　to　the　loading　of　materials　and　the　changes　in　shear　spring　stiffness　were　first　demonstrated　in　a　reasonable　operating　frequency　range.　Then　the　reasonable　operating　frequency　range　and　dynamics　of　the　resultant　nonlinear　flip-flow　vibrating　screen　(NFFVS)　with　piecewise　linear　springs　were　investigated　using　the　harmonic　balance　method　(HBM)　and　the　Runge-Kutta　numerical　method.　The　operating　frequency　region　for　the　NFFVS　lies　between　the　critical　frequency　omega　cs　and　the　frequency　omega　lb　corresponding　to　the　saddle-node　bifurcation　point.　Finally,　a　test　rig　was　designed　to　validate　the　theoretical　predictions.　Theoretical　and　experimental　results　demonstrate　that　piecewise　linear　springs　can　effectively　stabilize　the　relative　amplitude　of　the　FFVS.