In　this　paper,　the　bifurcation　of　periodic　solutions　for　a　four-dimensional　cubic　nonlinear　dynamic　system　with　a　center　singular　point　in　resonance　1:1　and　its　application　are　investigated.　The　existence　of　periodic　solutions　bifurcating　from　the　resonant　center　is　obtained　by　introducing　variables　transformation　and　defining　Poincare　map.　The　result　is　applied　to　investigate　the　periodic　motions　of　a　two-degree-of-freedom　composite　laminated　circular　cylindrical　shell.　The　existence　of　periodic　solutions　and　the　phase　portraits　under　a　group　of　parameter　condition　are　obtained　by　numerical　simulations,　which　verify　the　theoretical　results.