In　this　paper,　the　incremental　finite　element　equations　for　geometric　non-linear　analysis　of　piezoelectric　smart　structures　are　developed　using　a　total　Lagrange　approach　by　using　virtual　velocity　incremental　variational　principles.　A　four-node　first　order　shear　plate　element　model　with　reduced　and　selective　integration　is　also　developed.　Geometrically　non-linear　transient　vibration　response　and　control　of　plates　with　piezoelectric　patches　subjected　to　pulse　loads　are　investigated.　Active　damping　is　introduced　on　the　plates　by　coupling　a　self-sensing　and　negative　velocity　feedback　algorithm　in　a　closed　control　loop.　The　numerical　results　show　that　piezoelectric　actuators　can　introduce　significant　damping　and　suppress　transient　vibration　effectively.　The　effects　of　the　number　and　locations　of　the　piezoelectric　actuators　on　the　control　system　are　also　discussed.　(C)　2002　Elsevier　Science　Ltd.　All　rights　reserved.