Design of Vibration Isolation Structures with Minimum Compliance Using Multiple Types of Locally Resonant Acoustic Metamaterials via a Multiscale Topology Optimization Method

Designing structures that can isolate specified frequency ranges of vibration or noise while maintaining sufficient stiffness presents a significant challenge. Since locally resonant acoustic metamaterials (LRAMs) can create subwavelength bandgaps, this work proposes a multiscale topology optimization method for such structural designs utilizing multiple types of LRAM cells. To achieve the objectives, the methodology aims to minimize the dynamic responses at a specified point and the structural compliance at the macroscale. At the microscale, it aims to design microstructures with specified bandgaps and minimize macrostructural compliance. Compared to most existing methods, the LRAM design incorporated at the microscale in this approach can create specified bandgaps, enhancing the ability to control vibration isolation. The use of multiple types of LRAMs with bandgaps across different frequency ranges can extend the vibration isolation to a wider frequency range. Since the macrostructures consist of multiple microstructures and the microstructures are composed of various materials, a parameterized level-set-based multi-material approach is employed to optimize the topologies at both scales. The bandgap analysis during optimization is conducted using a homogenization framework. The efficacy of the method is demonstrated through numerical examples, which successfully generate structures capable of isolating vibrations within specified frequency ranges while maintaining minimal compliance. The method shows significant potential to design structures that are capable of effectively attenuating vibrations within a specified frequency range while maintaining load-bearing capacity.