Circularly symmetric normal modes of a circular drumhead

Plot[BesselJ[0,z],{z,0,30}]

α1=N[BesselJZero[0,1]]

t2=2 Pi/α1

RevolutionPlot3D[BesselJ[0,α1* r],{r,0,1},{θ,0,2Pi}]

Animate[
RevolutionPlot3D[BesselJ[0,α1* r]Cos[α1* t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,2Pi/α1},AnimationRunning->False]

α2=N[BesselJZero[0,2]]

t2=2Pi/α2

Animate[
RevolutionPlot3D[BesselJ[0,α2* r]Cos[α2* t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,2Pi/α2},AnimationRunning->False]

myframes=Table[
RevolutionPlot3D[BesselJ[0,α2* r]Cos[α2* t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,2Pi/α2,2Pi/α2/20}];

Export["NormalMode2.gif",myframes]

General normal modes of a circular drumhead

Plot[BesselJ[1,z],{z,0,30}]

Plot[BesselY[3,z],{z,0,30}]

α11=N[BesselJZero[1,1]]

Plot[BesselJ[1,α11*r],{r,0,1}]

RevolutionPlot3D[BesselJ[1,α11*r]*Cos[θ],{r,0,1},{θ,-Pi,Pi}]

t11=2 Pi/α1

RevolutionPlot3D[BesselJ[1,α11* r]Cos[θ],{r,0,1},{θ,0,2Pi}]

Animate[
RevolutionPlot3D[BesselJ[1,α11* r]*Cos[θ]*Cos[α11* t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,2Pi/α11},AnimationRunning->False]

α12=N[BesselJZero[1,2]]

t12=2Pi/α12

Animate[
RevolutionPlot3D[BesselJ[1,α12* r]*Cos[θ]*Cos[α12* t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,2Pi/α12},AnimationRunning->False]