The　periodic　motion　oi　a　simply-supported　rectangular　honeycomb　sandwich　plate　under　the　combination　oi　the　parametric　and　transverse　excitations　is　investigated　by　the　improved　iour-dimensional　subharmonic　Melnikov　method.　Based　on　periodic　transformations　and　Poincare　map,　a　lour-dimensional　subharmonic　Melnikov　function　is　obtained.　Then,　a　main　theorem,　which　can　be　used　to　determine　the　existence　oi　the　periodic　orbits　lor　the　four-dimensional　non-autonomous　nonlinear　dynamical　system,　is　presented.　The　periodic　motion　of　the　honeycomb　sandwich　plate　under　1:2　internal　resonance　is　then　studied　by　the　improved　method.　The　certain　parameter　regions　where　the　period-two　motion　may　occur　are　obtained.　Numerical　simulations　are　also　carried　out　to　verify　the　analytical　predictions.　©　2018　Journal　of　Dynamics　and　Control.　All　rights　reserved.