Vibration　energy　harvesting　can　be　designed　as　self-powered　devices　for　low-power　electronics　such　as　wireless　sensor　network　and　wearable　electronics.　Thus,　it　has　attracted　much　attention　in　recent　years.　In　this　work,　a　piezoelectric　vibration　energy　harvester　based　on　the　stepped　cantilever　beam　with　variable　thickness　under　magnetic　force　is　proposed.　First,　the　nonlinear　magnetic　force　is　introduced　and　the　energy　functions　are　obtained　by　using　Euler-Bernoulli　beam　theory.　The　Lagrange　equation　is　applied　to　establish　the　electromechanical　coupled　dynamic　equations.　Finally,　the　influence　of　the　distance　between　two　magnets　on　the　vibration　characteristics　of　the　system　is　examined.　Moreover,　the　mono-stable　and　bi-stable　responses　are　analyzed,　and　the　effects　of　the　distance　between　two　magnets　and　external　excitation　amplitude　on　the　vibration　and　voltage　responses　are　investigated.　It　can　be　concluded　that　the　distance　between　two　magnets　is　the　main　factor　affecting　the　potential　energy　of　the　system.　By　adjusting　this　distance,　mono-stable　and　bi-stable　responses　can　occur,　thus　effectively　improving　the　energy　harvesting　characteristics　of　the　piezoelectric　vibration　energy　harvester.　Compared　with　the　traditional　piezoelectric　energy　harvester　based　on　the　cantilever　beam　with　constant　cross-section,　the　proposed　piezoelectric　vibration　energy　harvester　based　on　the　stepped　cantilever　beam　with　variable　thickness　under　magnetic　force　exhibits　obvious　nonlinear　characteristics　and　achieves　broadband　frequency　responses　by　optimizing　the　structural　parameters.　©　2019,　Editorial　Department　Chinese　Journal　of　Solid　Mechanics.　All　right　reserved.