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## 2D membrane mode vibration

Nasser M. Abbasi

June 28, 2015

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This is a 2D animation of membrane vibrating in selected modes. This PDE is the 2D wave
PDE

Where is the amplitude of the wave. The region is 2D rectangle of sides which you can change
their values by using the sliders.

You can select the modes to excite and see an animation of the wave vibrating in that mode. The solution
to the above PDE is given by

Where the frequency is given by

To obtain the full solution, we would need to know the boundary conditions and initial conditions in
order to determine and . However, in this animation, when you select the mode to
excite, then the corresponding and terms are set to and all others terms are set to
zero.

For example, if you select to excite modes and then and
are set to and all other and terms are set to zero in the above double
summation. The animation supports up to 5 modes at most.

#### References

Professor Engelstad's Lecture notes. April 2, 2013. ME 740, Advanced Vibration. University of Wisconsin,
Madison.