Archive for the 'vibration' Category

29
Jun
07

Fundamental Modes of Vibration for a Sunset Moth-shaped membrane

Mode displacement plot of the 18th mode of a Sunset Moth-Shaped Membrane. NEiWorks. Just for fun.
27
Jan
06

Vibrating String with Damping

This analytical solution for a vibrating string was solved using the method of separation of variables assuming small linear perturbations. The rope was drawn using Mike Williams’ rope macro.

(* runtime: 2 seconds *)
c = 4; L = 1; h = 0.1; b = Pi; k := (n - 0.5)Pi/L; omega := Sqrt[(c k)^2 - (0.5b)^2];
Do[Plot[Evaluate[Sum[(6h/k^2)Sin[k/3] Exp[-0.5b t](Cos[omega t] + (0.5b/omega) Sin[omega t])Sin[k x], {n, 1, 10}]], {x, 0,L}, PlotRange -> {{0, L}, {-h, h}}, AspectRatio -> Automatic], {t, 0, 1.5, 0.025}];

28
Sep
04

Vibration Mode of a Spherical Membrane

Vibration Mode of a Spherical Membrane : This is a somewhat exaggerated example of how a spherical balloon might vibrate.

Vibration Mode of a Spherical MembraneMathematica 4.2, MathGL3d, 9/28/04

(* runtime: 4 seconds *)
Y := Re[SphericalHarmonicY[8, 4, theta, phi]]; r := (1 + 0.5Y);
ParametricPlot3D[{r Sin[theta] Cos[phi], r Sin[theta] Sin[phi], r Cos[theta], {EdgeForm[], SurfaceColor[Hue[Y]]}}, {theta, 0, Pi}, {phi, 0, 2Pi}, PlotPoints -> 72, Boxed -> False, Axes -> None]

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21
Apr
04

Fundamental Modes of Vibration for a Violin-Shaped Membrane

Mode displacement plots of the 19th, 28th, and 45th modes, respectively, from left to right, computed with GeoStar 2.8.Click here to see a holographic interferogram of a real violin.
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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