WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Chapter 3
Bandgap structures as optimal designs
It can be concluded from the study of simple mass-spring structures that a large
reduction of the vibration level can be obtained if the structure is created from a
periodic material – a bandgap structure. One question then naturally arises: ”Are
bandgap structures then optimal for quenching vibrations?”. The answer is in many
cases yes and periodic-like structures often appear as optimal designs. Whether this
is the case depends on the contrast of the material properties and the dimensions of
the structure relative to the frequency of vibrations.
This chapter presents optimized designs for different types of mechanical and
acoustic structures. All results are based on FE continuum models combined with
gradient-based topology optimization.
Thesis papers [4]–[9]
Paper [4] presents a study of the optimal layout of two elastic materials in a planar
two-dimensional continuum structure that is subjected to forced in-plane vibrations.
The author’s contribution to the paper focuses on design of structures that quench
vibrations. Specialemphasisisputonaninvestigationofhowtheoptimizedmaterial
layout depends on the contrast between material properties and the effect of different
loading conditions. Additionally, the possibility of creating elastic waveguiding
structures is explored.
Paper [5] also deals with optimization of the layout of two elastic materials in a
planar two-dimensional structure. Here, the structure is subjected to a steady-state
pressure or shear wave propagating in multiple directions. Special focus is put on
investigating how themateriallayout depends onthewavelength ofthewave relative
to the dimensions of the structure.
Paper [6] follows up on the work initiated in paper [5]. Two-dimensional material
layouts are obtained for the case of multi-frequency pressure and shear waves.
Moreover, the optimization algorithm is extended to allow for distributing three
materials in the structure. The paper also considers the design of structures that
maximize the absorption of waves with two or three materials available.
Paper [7] considers the problem of vibration quenching from another perspective.
Instead of minimizing vibration levels or wave amplitudes, the eigenfrequencies of
the structure are explored. The paper demonstrates that bandgap structures can
be created by maximizing the separation of two adjacent eigenfrequencies. The
connection between the material properties and the maximum possible separation
of eigenfrequencies is investigated as well.
17