Abstract
Sonic or acoustic metamaterials may offer a mechanically robust and highly customizable solution to open large band gaps in the low-frequency dispersion spectrum of beam lattice materials. Achieving the largest possible stop bandwidth at the lowest possible center frequency may be a challenging multi-objective optimization issue. The paper presents a first effort of analysis, systematization and synthesis of some recent multi-disciplinary studies focused on the optimal spectral design of beam lattice materials and metamaterials. The design parameter vector is a finite set including all the microstructural properties characterizing the periodic material and the local resonators. Numerical algorithms are employed as leading methodology for solving various instances of the optimization problem. Methodological alternatives, based on perturbation methods and computational modeling, are also illustrated. Some optimal results concerning the dispersion spectrum of hexachiral, tetrachiral and anti-tetrachiral materials and metamaterials are summarized. The concluding remarks are accompanied by preliminary ideas to overcome some operational issues in solving the optimization problem.
Highlights
An increasing research attention is being currently paid to the characterization of the acoustic properties of periodic materials with beam lattice microstructure
The present paper represents a first effort of multi-disciplinary analysis, systematization and synthesis of several analytical formulations and numerical results achieved by the authors in recent studies on the optimal spectral design of beam lattice materials and metamaterials
The constrained optimization problem is found not to have an admissible solution corresponding to a full band gap between the acoustic and optical surfaces
Summary
An increasing research attention is being currently paid to the characterization of the acoustic properties of periodic materials with beam lattice microstructure. Sonic or acoustic metamaterials offer a mechanically robust and highly customizable solution to open band gaps in the dispersion spectrum of beam lattice materials, without compromising the load bearing capacity given by the microstructural stiffness. Optimal Spectral Design of Acoustic Metamaterials between the periodic material and auxiliary oscillators (local resonators) elastically connected to the cellular microstructure (Liu et al, 2000, 2005; Huang et al, 2009; Mei et al, 2012; Zhu et al, 2012; Krushynska et al, 2014, 2017). The present paper represents a first effort of multi-disciplinary analysis, systematization and synthesis of several analytical formulations and numerical results achieved by the authors in recent studies on the optimal spectral design of beam lattice materials and metamaterials. A dynamic linear model suited to parametrically describe the free propagation of elastic waves in non-dissipative beam lattice materials and acoustic metamaterials is presented (section 2). Concluding remarks and some possible future developments are pointed out
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