WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

wave-guiding properties show promising results [4, 5, 6]. This paper presents a status of the research
project dealing with the design of optimized structures and provides an outlook on further
research.
Vibrations in an elastic bar: Theory and experiments
To test the computational model and study the basic phenomenon a simple experiment has been
performed. The theoretical predictions of frequency responses were checked experimentally using
a laboratory model of an elastic bar and the setup shown in Fig. 2. Here, an input signal is fed to
a vibration shaker, which transmits vibrations to the bar across a force transducer. Elastic waves
then propagate through the bar, where end movements are picked up by an accelerometer.
We tested elastic bars made of periodic sections of Brass-PMMA or Aluminium-PMMA, both
exhibiting band gaps. The results described here are for the bar shown in Fig. 2, made of fiveand-a-half
repetitions of a base section consisting of two bars of circular cross section, one of
Aluminium and one of PMMA, both having diameter 10 mm and length 75 mm, and with bar
pieces glued end-to-end using Araldite 2011 epoxy structural adhesive.
Fig. 3(left) is a typical frequency response for this periodic bar, showing two pronounced band
gaps with a response drop-off about 40 dB compared with the non-resonant, low-level response
outside the band gaps. Fig. 3(right) shows the corresponding theoretical predictions from the computational
program. Reasonable agreement is noted, both with regards to the resonance tops but
more importantly with respect to the response drop in the band gap frequency ranges. The noise in
the experimental curves in the band gaps originates in the noise limit of the experimental setup.
Figure 2: Experimental setup and part of the setup showing (from left to right) the vibration exciter,
force transducer, periodic bar system with supporting threads, and accelerometer.
Additional experiments are planned in order to study the vibrational response of 2D periodic and
optimized structures as well as of micro-size structures.
The topology optimization method
The topology optimization technique, see e.g. [7], can with advantage be used to design multiphase
structures with optimized vibrational and wave-transmitting properties. Using this method
for the steady-state dynamical problem involves, in addition to e.g. a compliance problem, additional
difficulties due the complex FE equations, possible wave-transmitting boundary conditions,
and/or structural damping.
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