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Structural and Multidisciplinary Optimization

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12-01-2021 | Research Paper

High natural frequency gap topology optimization of bi-material elastic structures and band gap analysis

Authors: Heitor Nigro Lopes, Jarir Mahfoud, Renato Pavanello

Published in: Structural and Multidisciplinary Optimization | Issue 5/2021

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Abstract

This work aims to perform the topology optimizationof frequency separation interval of continuous elastic bi-dimensional structures in the high-frequency domain. The studied structures are composed of two materials. The proposed algorithm is an adaptation of the Bidirectional Evolutionary Structural Optimization (BESO). As the modal density is high in this frequency domain, the objective function, based on the weighted natural frequency, is formulated to consider an important number of modes. To implement the algorithm, a mode tracking method is necessary to avoid problems stemming from mode-shifting and local modes. As the obtained results by using structural dynamics analysis present quasi-periodic topology, further calculations are done to compare the results with and without imposed periodicity. A dispersion analysis based on wave propagation theory is performed by using the unit cell previously obtained from the structural optimization to investigate the band gap phenomenon. The resulting band gaps from the dispersion analysis are compared with respect to the dynamic behavior of the structure. The topology optimization methodology and the wave propagation analysis are assessed for different boundary conditions and geometries. Comparison between both analyses shows that the influence of the boundary conditions on the frequency separation interval is small. However, the influence from the geometry is more pronounced. The optimization procedure does not present significant numerical instability. The obtained topologies are well-defined and easily manufacturable, and the obtained natural frequency separation intervals are satisfactory.

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Title: High natural frequency gap topology optimization of bi-material elastic structures and band gap analysis
Authors: Heitor Nigro Lopes
Jarir Mahfoud
Renato Pavanello
Publication date: 12-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 5/2021
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-020-02811-0

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