Maximizing spatial decay of evanescent waves in phononic crystals by topology optimization

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

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Band structure of evanescent waves in phononic crystals

2008 IEEE Ultrasonics Symposium ◽

10.1109/ultsym.2008.0061 ◽

2008 ◽

Author(s):

Vincent Laude ◽

Boujemaa Aoubiza ◽

Younes Achaoui ◽

Sarah Benchabane ◽

Abdelkrim Khelif

Keyword(s):

Band Structure ◽

Evanescent Waves ◽

Phononic Crystals

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Topology optimization of two-dimensional phononic crystals using FDTD and genetic algorithm

2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA) ◽

10.1109/spawda.2011.6167278 ◽

2011 ◽

Author(s):

Xiao-Xing Su ◽

Tian-Xue Ma ◽

Hao-Wen Dong ◽

Yue-Sheng Wang

Keyword(s):

Genetic Algorithm ◽

Topology Optimization ◽

Phononic Crystals ◽

Two Dimensional

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Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

10.31224/osf.io/nb2vz ◽

2021 ◽

Author(s):

Atul Kumar Sharma ◽

Gal Shmuel ◽

Oded Amir

Keyword(s):

Topology Optimization ◽

Electric Fields ◽

Computational Cost ◽

Optimization Method ◽

Phononic Crystals ◽

Frequency Bands ◽

Design Variables ◽

Gradient Based ◽

Soft Dielectrics ◽

Design Freedom

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider than those obtained from the previous metaheuristics-based method, while the computational cost to identify them is reduced by orders of magnitude.

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