WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Relations to recent work 51
Figure 5.9 Illustration of the compression of the pulse as it propagates through a spacetime
optimized structure. From paper [21].
these canbe partlyremoved if anexplicit penalizationterm is added to the objective
function, although this generally causes the output pulse to deviate more from the
target output.
It turns out that if the two involved materials have different stiffness and mass
density the possibility for manipulating the wave is greater. This however depends
on the specific values of the parameters. An additional complication arises if the
mass density varies in time. Then it becomes necessary to use a more sophisticated
time-integration routine that is able to handle time-discontinuous velocity fields.
Relations to recent work
Optimization of dynamic systems in finite frequency ranges with Padé approximants
was recently used by Donoso and Sigmund (2009). They considered the distribution
of piezo-electric material in order to optimize the dynamic response of a mechanical
structure.
The system of non-linear oscillators studied in paper [19] has been further examined
by Rothos and Vakakis (2009) who studied wave interaction in the case of
essentially nonlinear oscillators. They did not consider optimization.