2D Wave Propagation
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.
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 .