WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Design of multi-phase structures with optimized vibrational and
wave-transmitting properties
Jakob S. Jensen ∗ , Ole Sigmund and Jon J. Thomsen
Department of Mechanical Engineering, Solid Mechanics
Technical University of Denmark, Lyngby, Denmark
e–mail: jsj@mek.dtu.dk
Martin P. Bendsøe
Department of Mathematics
Technical University of Denmark, Lyngby, Denmark
Summary In this paper we show the status of a research project dealing with optimization of vibration
and wave-propagation in multi-phase structures. We present experimental and theoretical results and point
out directions for further research.
Introduction
Band gap materials have received considerable attention in the last decade, see e.g. [1]. A periodic
arrangement of materials with different physical properties may cause gaps to appear in the classical
band structures—corresponding to ranges of frequencies for which waves cannot propagate.
The waves may be electromagnetic or elastic, with the corresponding band gap materials referred
to as photonic and phononic, respectively.
Structures made from a band gap material have several interesting applications, e.g. as parts of
mechanical filters and resonators and in optical wave guides and lasers. A FE-program has been
developed to analyze steady-state vibration and/or wave-propagation in periodic structures. As an
example we show the vibrational behavior of an elastic band gap structure shown in Fig. 1. The
periodic material has here been designed so that a band gap exists in the frequency range around
40 kHz and the corresponding frequency response is seen to be significantly reduced near this frequency.
Currently, the computational model is being extended to cover also 3D structures and has
also been used to study the behavior of periodic mass-spring structures [2].
Acceleration response (dB)
120
100
80
60
40
20
0
-20
periodic
-40
pure epoxy
-60
pure alu
0 10 20 30 40 50 60 70 80 90 100
Excitation frequency (kHz)
Figure 1: A structure composed of 10×10 square aluminum inclusions in epoxy subjected to periodic
loading at the left boundary and the corresponding frequency response at the right boundary.
To facilitate the design of optimized structures a topology optimization code has been developed.
Recently the topology optimization technique was applied successfully to the design of band gap
materials [3], and the first results for designing structures with optimized wave-reflecting and
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