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Design of phononic crystals for self-collimation of elastic waves using topology optimization method

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Abstract

Self-collimating phononic crystals (PCs) are periodic structures that enable self-collimation of waves. While various design parameters such as material property, period, lattice symmetry, and material distribution in a unit cell affect wave scattering inside a PC, this work aims to find an optimal material distribution in a unit cell that exhibits the desired self-collimation properties. While earlier studies were mainly focused on the arrangement of self-collimating PCs or shape changes of inclusions in a unit cell having a specific topological layout, we present a topology optimization formulation to find a desired material distribution. Specifically, a finite element based formulation is set up to find the matrix and inclusion material distribution that can make elastic shear-horizontal bulk waves propagate along a desired target direction. The proposed topology optimization formulation newly employs the geometric properties of equi-frequency contours (EFCs) in the wave vector space as essential elements in forming objective and constraint functions. The sensitivities of these functions with respect to design variables are explicitly derived to utilize a gradient-based optimizer. To show the effectiveness of the formulation, several case studies are considered.

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant (No: 2014–021950) funded by the Korean Ministry of Education, Science and Technology (MEST), Basic Science Research Program through NRF funded by the Korean Ministry of Education (No: 2014–048162), contracted through Institute of Advanced Machinery and Design at Seoul National University and the Global Frontier R&D Program on Center for Wave Energy Control based on Metamaterials funded by the NRF under the Ministry of Science, ICT & Future Planning, Korea (No: 2014–063711).

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Authors and Affiliations

  1. WCU Multiscale Mechanical Design Division, School of Mechanical and Aerospace Engineering, Seoul National University, 599 Gwank-ro, Gwanak-gu, Seoul, 151-742, South Korea

    Jun Hyeong Park & Yoon Young Kim

  2. Samsung Advanced Institute of Technology, 130 Samsung-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do, 443-803, South Korea

    Pyung Sik Ma

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  1. Jun Hyeong Park
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  2. Pyung Sik Ma
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Correspondence to Yoon Young Kim.

Additional information

The main idea of this work was first presented at WCSMO10 (May 19–24, 2013, Orlando, Florida, USA) under the title of “Topology Optimization of Phononic Crystals for Self-collimation of Elastic Waves” by the authors.

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Park, J.H., Ma, P.S. & Kim, Y.Y. Design of phononic crystals for self-collimation of elastic waves using topology optimization method. Struct Multidisc Optim 51, 1199–1209 (2015). https://doi.org/10.1007/s00158-014-1206-8

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  • DOI: https://doi.org/10.1007/s00158-014-1206-8

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