This　paper　is　focused　on　the　nonlinear　breathing　vibrations　of　the　circular　mesh　antenna　based　on　a　composite　laminated　circular　cylindrical　shell　with　radially　pre-stretched　membranes　at　both　ends　and　clamped　along　a　generatrix.　The　finite　element　model　of　the　circular　mesh　antenna　are　established,　we　study　the　effects　of　different　mesh　stiffness　on　the　first　six　orders　frequencies.　It　is　found　that　there　is　an　approximate　threefold　relationship　between　the　first-order　frequency　and　the　forth-order　frequency.　Based　on　the　particular　integer　multiple　relationship,　we　can　conclude　that　there　is　the　1:3　resonance　between　the　first-order　and　the　forth-order　vibrations　of　the　circular　mesh　antenna.　The　method　of　multiple　scales　is　employed　to　obtain　the　four-dimensional　nonlinear　averaged　equation　based　on　the　two　degree　of　freedom　non-autonomous　nonlinear　equations　of　the　equivalent　model　of　circular　mesh　antenna　and　the　1:3　internal　resonance　is　considered　here.　Then,　based　on　the　numerical　method,　the　chaotic　dynamics　of　the　equivalent　model　of　circular　mesh　antenna　are　studied　by　the　bifurcation　diagrams,　the　phase　portraits,　the　waveforms,　the　power　spectrums　and　the　Poincaré　map.　The　temperature　parameter　excitation　shows　that　the　complex　chaotic　phenomena　occur　under　the　certain　initial　conditions.　©　Published　under　licence　by　IOP　Publishing　Ltd.