10
Nov
03

Mode of Vibration of a Circular Membrane

31st Fundamental Mode of Vibration of a Circular Membrane. This is an example of how a circular drumhead might vibrate. Click here to see a rotatable animated version.
J3(k43r)cos(3θ) → frequency: f31 = f1k43/k10 = 6.74621 f1

(* runtime: 5 seconds *)
Clear[r]; << NumericalMath`BesselZeros`;
k = BesselJZeros[3, 4][[4]];
<< MathGL3d`OpenGLViewer`;
texture = Graphics[{RGBColor[0, 1, 1], Rectangle[{0, 0}, {10, 10}], RGBColor[0.5, 0, 1], Rectangle[{1, 1}, {9, 9}]}];
MVShow3D[ParametricPlot3D[{r Sin[theta], r Cos[theta], 0.25BesselJ[3, k r]Cos[3 theta]}, {r, 0, 1}, {theta, 0, 2Pi}, PlotPoints -> {56, 168}], MVNewScene -> True, MVTexture -> texture, MVTextureMapType -> MVMeshUVMapping, MVScaleTexture -> {14, 42}]

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