Constructing continuum models of acoustic metamaterials via the symbiotic organisms search (SOS) optimization

Based on the symbiotic organisms search (SOS) optimization algorithm, a robust strain gradient (SG) continuum model has been proposed to accurately capture the broadband dispersion relations of one-dimensional acoustic metamaterials. Under the continuous assumption, an unavoidable key step is the Taylor expansion of displacements, which directly influences the accuracy of the corresponding continuum theory. When the wavelength becomes comparable to the periodic characteristic size, the coefficients of Taylor expansions need necessary adjustments due to the discreteness of the microstructure. Thus, the continuum theories still face critical challenges in predicting the broadband dispersion feature. This remains widely open so far. In this study, we attempt to adopt the SOS optimization to determine the optimal Taylor expansion coefficients to guarantee the dispersion diagrams causing the minimal error throughout the first Brillouin zone. The robustness of the SOS-based SG continuum model is demonstrated with three benchmark examples, i.e., the monoatomic, diatomic, and mass-in-mass lattices. Such an attempt of constructing continuum models with the help of optimization tools may shed some new light on continuum mechanics of structure media.