Systematic design of phononic band–gap materials and structures by topology optimization

Abstract

Phononic band-gap materials prevent elastic waves in certain frequency ranges from propagating, and they may therefore be used to generate frequency filters, as beam splitters, as sound or vibration protection devices, or as waveguides. In this work we show how topology optimization can be used to design and optimize periodic materials and structures exhibiting phononic band gaps. Firstly, we optimize infinitely periodic band-gap materials by maximizing the relative size of the band gaps. Then, finite structures subjected to periodic loading are optimized in order to either minimize the structural response along boundaries (wave damping) or maximize the response at certain boundary locations (waveguiding).

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

“…Multiphysics problems, where coupled analyses are required, are promising applications due to the inherent difficulties in obtaining good designs intuitively, and thus recently more research has been conducted in this area [2,3,4,5,6]. These applications, however, have mostly been restricted to problems where the multi-physics behavior is limited to the material-part of the design.…”

Morphology-based black and white filters for topology optimization

“…Usually, the post-processed structure has a performance that is very close to the optimized structure. However, recently the author's research group has applied the topology optimization to phononic and photonic crystal design (Sigmund and Jensen, 2003;Jensen and Sigmund, 2004) where structures with intricate semi-periodic patterns appear as the result of the topology optimization process. An example of the design of a nano-scale optical splitter from Borel et al (2005) is shown in Fig.1b.…”

On Optimum Design and Periodicity of Band-Gap Structures

“…The resonance peaks can be removed or reduced by including some damping, and we also found that there is no significant change of the band-gap behavior for relatively small damping. The effect of smoothing by including damping is often used in the topology optimization of band-gap structures [7].…”

“…Due to a wealth of potential applications in vibration protection, noise isolation, waveguiding, etc., the study and development of bandgap rod, mass-spring, beam, grillage, disk and plate structures, in most cases by topology optimization, have attracted increasing attention in recent years, see e.g. [5,[7][8][9][10][11][12][13][14][15][16][17][18]. Elastodynamics of finite or infinite periodic 1D rod or beam structures has been studied in [6,[19][20][21].…”

“…An abundance of other references is available in the exhaustive textbook [31]. The problem of minimization of forced vibration response of structures subjected to external time-harmonic loading has been studied in, e.g., [7,17,29,[32][33][34].…”