Thin Plate Convergence Rate


Raw Data

Methodology:
Three sets of time step sizes are chosen: the step size being 1/200th of the
period of driving force; 1/2000th of the period of the driving force, and
1/20000th of the period of the driving force.
The plate is driven to a stable cyclical state in one frequency first, and
the driving force is switched to a different frequency, and the response and
convergence is then observed as the plate settles into the second frequency.

Files under the directory covergenceTrend_stepsize_1_[200|2000|20000]th_Period/
are results taken from the step sizes being 1/[200|2000|20000]th of the
period of the driving force. The file convergencePlot[x]to[y] shows the
timestep taken Vs response Vs convergence as the driving force's requency is
switched from x to y.

Explanation of terms:
A window is a history of the total energy of the plate
during a past length of time. The length of time is chosen
to be the period of the driving force.
A response is the highest element in the window.
The convergence is the two-norm of the difference
between the FFT coefficient vector obtained using the
current window and the FFT coefficient vector obtained
using some earlier window.

Summary of results:
The response (not convergence) of a given frequency stabilises after
a certain amount of simulated time. It turned out to be about the same
for all frequencies (around 22 units of simulated time.)
The size of a timestep doesn't affect the value of the response, as
long as it is greater than 1/100th of the period of the driving force.
However, taking a timestep size that is larger than 1/40,000th of the
period of the driving force makes the window curve look like a noisy
sine wave, therefore the convergence does not settle down.
Finally, it doesn't matter what the previous configuration of the
plate was in: it takes roughly the same amount of simulated time for
a plate to settle down in to the new configuration.