In　this　paper,　the　nonlinear　traveling　wave　vibrations　are　investigated　for　the　graphene-reinforced　porous　aluminum-based　sandwich　rotating　conical　(GRPA-SRC)　shell　with　the　arbitrary　boundary　conditions.　The　material　of　the　rotating　conical　shell　is　the　sandwich　structure　composed　of　the　graphene-reinforced　porous　aluminum-based　(GRPA)　material.　Two　surfaces　of　the　rotating　conical　are　made　of　the　metallic　aluminum　and　central　core　layer　is　the　GRPA.　There　are　three　graphene　distribution　types　and　three　porosity　distributions　applied　to　the　nonlinear　vibration　analysis.　We　consider　the　comprehensive　effect　of　combining　the　transverse　harmonic　excitation　and　in-plane　load　on　the　nonlinear　traveling　wave　vibrations　of　the　rotating　conical　shells.　The　first-order　shear　deformation　theory　(FSDT)　and　von　Karman　nonlinear　strain-displacement　relations　are　employed　in　the　structural　modeling.　The　effects　of　Coriolis　forces　and　initial　hoop　tensions　are　considered　to　obtain　the　kinetic　energy,　potential　energy　and　external　force　work.　Since　the　vibration　form　of　the　rotating　conical　shell　is　the　traveling　wave　vibration,　the　trigonometric　functions　are　used　to　represent　the　mode　in　the　circumferential　direction.　Chebyshev　polynomials　are　used　to　solve　the　axial　direction.　Further　utilizing　energy　principle,　the　nonlinear　ordinary　differential　equations　are　obtained　for　the　GRPA-SRC　shell　with　two　degrees　of　freedom.　The　amplitude-frequency　response　curves,　force-amplitude　response　curves,　bifurcation　diagrams,　maximum　Lyapunov　exponent,　waveforms,　phase　portraits　and　Poincare　map　of　the　GRPA-SRC　shell　are　calculated　by　using　Runge-Kutta　method.　Adding　the　springs　at　both　ends　of　the　GRPA-SRC　shell　can　simulate　the　arbitrary　boundary　conditions.　During　the　solution　process,　the　circumferential　direction　of　the　GRPA-SRC　shell　is　represented　by　the　trigonometric　function,　and　direction　of　the　generatrix　is　denoted　by　using　Chebyshev　polynomials.　The　arbitrary　boundary　conditions　are　obtained　for　changing　the　spring　potential　energy.　This　work　is　expected　to　provide　the　practical　value　for　the　nonlinear　vibrations　of　the　graphene-reinforced　porous　metal　rotating　shell　with　the　arbitrary　boundary　conditions.