Numerical study and topology optimization of 1D periodic bimaterial phononic crystal plates for bandgaps of low order Lamb waves.

The optimum topology of bimaterial phononic crystal (PhCr) plates with one-dimensional (1D) periodicity to attain maximum relative bandgap width of low order Lamb waves is computationally investigated. The evolution of optimized topology with respect to filling fraction of constituents, alternatively stiff scattering inclusion, is explored. The underlying idea is to develop PhCr plate structures with high specific bandgap efficiency at particular filling fraction, or further with multiscale functionality through gradient of optimized PhCr unitcell all over the lattice array. Multiobjective genetic algorithm (GA) is employed in this research in conjunction with finite element method (FEM) for topology optimization of silicon-tungsten PhCr plate unitcells. A specialized FEM model is developed and verified for dispersion analysis of plate waves and calculation of modal response. Modal band structure of regular PhCr plate unitcells with centric scattering layer is studied as a function of aspect ratio and filling fraction. Topology optimization is then carried out for a few aspect ratios, with and without prescribed symmetry, over various filling fractions. The efficiency of obtained solutions is verified as compared to corresponding regular centric PhCr plate unitcells. Moreover, being inspired by the obtained optimum topologies, definite and easy to produce topologies are proposed with enhanced bandgap efficiency as compared to centric unitcells. Finally a few cases are introduced to evaluate the frequency response of finite PhCr plate structures produced by achieved topologies and also to confirm the reliability of calculated modal band structures. Cases made by consecutive unitcells of different filling fraction are examined in order to attest the bandgap efficiency and multiscale functionality of such graded PhCr plate structures.
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