2D Wave Propagation

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This Demonstration shows the solution of the two-dimensional wave equation subjected to an instantaneous hammer hit centered at the source point location with zero initial displacement and velocity. You can choose free or fixed boundary conditions. A fast and accurate solution was obtained by using the orthogonal function expansion method. By decreasing the aspect ratio, the solution approaches the one-dimensional approximation.

Contributed by: Jason Beaulieu and Brian Vick (May 2012)
Open content licensed under CC BY-NC-SA


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Details

The dimensionless 2D wave equation can be written

.

The fixed boundary conditions are

, , , .

The free boundary conditions are

, , , .

The initial conditions are

and at .

Using Fourier analysis, we can transform each forcing function and the differential equation to create a solution in the form of

,

where and are the respective eigenfuntions and is the transformation of .



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