Topology Optimization of Resonant Structures for Locally Resonant Elastodynamic Metasurfaces

Open Access
- Author:
- Giraldo Guzman, Daniel
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2024
- Committee Members:
- Robert Kunz, Professor in Charge/Director of Graduate Studies
Yun Jing, Outside Unit Member
Parisa Shokouhi, Dissertation Co-Advisor
Michael Roan, Major Field Member
Clifford Lissenden, Outside Field Member
Mary Frecker, Chair & Co-Dissertation Advisr
Amanda Hanford, Major Field Member - Keywords:
- Topology optimization
locally resonant metamaterials
surface waves
plate waves - Abstract:
- This research presents a systematic design methodology for resonant structures exhibiting particular dynamic responses by implementing a two-fold eigenfrequency-based approach to match antiresonances with target frequencies subject to harmonic loads and to generate resonance gaps around specific frequencies. This design methodology, formulated as gradient-based density-based topology optimization, introduces a computationally efficient approach for 3D dynamic problems requiring resonance or antiresonance manipulation by combining classical eigenfrequency design approaches with a novel harmonic-informed eigenmode identification strategy. The optimization’s objective function minimizes the error between target antiresonances and the actual structure’s antiresonance eigenfrequencies, and maximizes the difference between a prescribed frequency and all neighbor resonance eigenfrequencies. The harmonic analysis-informed identification strategy compares harmonic displacement fields against eigenvectors using a modal assurance criterion, ensuring an accurate recognition and selection of appropriate eigenmodes. Simultaneously, this design methodology effectively prevents well-known problems in topology optimization of eigenfrequencies such as localized eigenmodes, repeated eigenfrequencies, and eigenmodes switching order; a new eigenmode identification approach removes these problems by analyzing the eigenvectors’ response. Multiple case studies demonstrate that the proposed design methodology generates resonant structures exhibiting specific resonances and antiresonances at the desired frequencies subject to multiple harmonic loads, given different design domain dimensions, mesh discretizations, or material properties. The developed methodology enables the design of elastic/acoustic metamaterials without relying on commonly used dispersion curves design methodologies and, presents a computationally efficient approach to conceiving metamaterials by designing single resonant units, instead of unit cells that require periodicity and several assumptions. Multiple numerical and experimental studies demonstrate the optimized resonators' effectiveness in controlling surface and plate wave propagation when arranged as locally resonant metasurfaces.