Maximizing bandgap width and in-plane stiffness of porous phononic plates for tailoring flexural guided waves: Topology optimization and experimental validation

摘要

Phononic crystal plates (PhPs) with porous heterogeneities manufactured through perforation of a uniform plate comprise effective wave reflecting interfaces and are free from complexities and interfacial imperfections associated with fabricating bi-material designs. However, numerical optimization of such porous PhPs for maximized bandgap efficiency naturally leads to topologies with isolated solid domains, or disconnected island-like features. Requiring PhPs to exhibit an adequate stiffness is, therefore, an important design consideration. This paper presents a multi-objective topology optimization study with experimental validation to explore the relationship between bandgap efficiency and effective in-plane stiffness, introducing topologies exhibiting superior properties compared to those reported in earlier works. Topology optimization is performed in two stages: first, at a relatively coarse resolution followed by a topology optimization on a refined mesh. The minimum allowable length scale of features is maintained across the mesh refinement, and thus the refined stage primarily leads to optimization of the feature boundaries, which is shown to significantly enhance response. Bandgap of fundamental flexural guided wave modes is studied herein, and it is shown how bandgap efficiency is degraded by increasing the in-plane stiffness. Distinct stiff and compliant topology modes are realized in the intermediate section of the optimized Pareto fronts which offer variation of structural stiffness while having almost the same bandgap efficiency, with potential application as base cells in design of gradient phononic lattices. A subset of promising stiff and compliant optimized topologies are manufactured by water-jetting of an aluminum plate and experimentally tested to validate the calculated bandgap efficiencies and effective elastic properties. (C) 2016 Elsevier Ltd. All rights reserved.