The　advanced　three-dimensional　braided　composite　structure　has　excellent　integrity,　which　can　effectively　avoid　the　problems　of　interlayer　stress　jump　and　interface　debonding　that　may　occur　in　traditional　composite　laminated　structures.　However,　most　of　the　existing　references　on　the　three-dimensional　braided　composite　structure　are　fragmented,　and　there　is　little　research　on　their　vibrations.　Taking　the　cylindrical　shell　of　a　rocket　as　the　object　and　considering　the　complex　flight　environment,　a　general　framework　for　the　vibration　problems　of　the　three-dimensional　braided　composite　shell　is　proposed　for　the　first　time.　The　equivalent　mechanical　parameters　of　the　three-dimensional　braided　composite　material　are　calculated　based　on　the　volume　averaging　method.　Then,　the　nonlinear　dynamic　model　of　the　three-dimensional　braided　composite　cylindrical　shell　is　established,　and　the　natural　vibration　characteristics　are　analyzed.　Under　the　case　of　1:1　internal　resonance,　the　pseudo-arc　length　continuation　method　is　used　to　solve　the　nonlinear　resonant　responses　of　this　nonlinear　system.　Finally,　we　apply　the　fourth-order　Runge-Kutta　algorithm　to　study　the　chaotic　dynamics　of　the　three-dimensional　braided　composite　cylindrical　shell　model.　This　framework　presented　in　this　paper　can　be　extended　to　the　study　of　nonlinear　vibrations　and　chaotic　dynamics　of　other　three-dimensional　braided　composite　structures.　©　2024　Elsevier　Masson　SAS