WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

50 Chapter 5 Advanced optimization procedures
Figure 5.7 Instantaneous material distribution and wave motion for the optimized structure
at t = 5.0s and t = 5.4s. From paper [20].
Displacement
1
0.8
0.6
0.4
0.2
0
input
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time
output
output - uncompr.
Figure 5.8 Input wave pulse and compressed wave pulse for an optimized structure. For
comparison the uncompressed output wave pulse is shown too. From paper [21].
compared to the optimized static design. Interestingly, this improvement is not
facilitated by an increased reflection. On the contrary, the reflected wave energy is
reduced from 17% to only 1%. Instead wave energy is extracted from the system
by the action of the external forces that must be present in order to change the
stiffness at each structural position in time.
Other possibilities for wave manipulation appear when it is possible to change
the structural properties in time as well as in space. In the second example the
aim of the optimization procedure is to minimize the difference between the output
pulse and a specified target output. Fig. 5.8 shows an example of the compression
of a Gaussian pulse when it propagates through an optimized dynamic structure.
Shown for comparison are also the input wave pulse and an uncompressed output
wave pulse. It should be noted that for a static linear structure such a compression
is not possible, since it involves changing the frequency contents of the pulse.
A further illustration of the compression of the pulse along with instantaneous
plots of the material distribution is shown in Fig. 5.9. The compression of the pulse
is created by the stiffer material moving along with the rear tail of the wave. In this
case the design variables generally attain intermediate optimized values. However,