Topological Optimization of Phononic Crystal Thin Plate by a Genetic Algorithm.

Phononic crystal structures are designed to control sound and mechanical wave propagation. Prior research has demonstrated that periodic arrangements of materials can create band gaps where wave transmission is suppressed. However, the relationship between structural parameters and resulting band gaps remains unclear in many configurations. Traditional design approaches rely on trial and error or limited parametric studies. This gap motivated the use of computational optimization techniques to systematically explore design variables. Adaptive genetic algorithms have been proposed as a tool for topology optimization in various engineering domains. No prior work had resolved how polymerization degree or symmetry influences band gap formation in thin plates. This paper contributes by applying GA to phononic crystal thin plates composed of aluminum and epoxy resin. The study aims to identify key design factors that influence band gap characteristics.

This study aims to optimize the topology of phononic crystal thin plates using a genetic algorithm. The goal is to identify structural parameters that maximize band gap formation. The specific problem addressed is the lack of a systematic approach to design phononic crystal thin plates with desired acoustic properties. The motivation stems from the need for efficient sound insulation materials in engineering applications. The study focuses on thin plates composed of aluminum and epoxy resin. The researchers seek to determine how material parameters and structural configurations influence band gaps. By applying a genetic algorithm, the study aims to automate the design process. The approach allows exploration of a wide range of topologies that would be impractical to test manually.

The study employs a genetic algorithm for topology optimization of phononic crystal thin plates. The algorithm uses adaptive rates for crossover and mutation based on population diversity. Plane wave expansion method is applied to calculate band gaps for each generated structure. Fourier displacement property is used to compute the structure function in the PWE calculations. The optimization process iteratively evolves topologies to maximize band gap width. Material parameters for aluminum and epoxy resin are defined based on known mechanical properties. The algorithm evaluates each design based on its band gap characteristics. The study systematically varies filling rates, symmetry, and polymerization degree to assess their impact.

The genetic algorithm successfully identifies optimal topologies for phononic crystal thin plates. Results show that filling rates significantly influence band gap formation in the structures. Symmetry of the design is found to correlate with the width and position of band gaps. Polymerization degree is identified as a critical factor in determining structural performance. Material parameters of aluminum and epoxy resin are confirmed to affect band gap characteristics. The adaptive GA method demonstrates improved convergence compared to fixed-rate approaches. The study reveals that higher filling rates generally lead to wider band gaps in the structures. The relationship between symmetry and band gap position is quantified through multiple iterations.

The authors propose that adaptive genetic algorithms are effective for optimizing phononic crystal thin plate designs. The study confirms that filling rates, symmetry, and polymerization degree are key design factors. The results suggest that material parameters must be carefully selected for optimal performance. The researchers observe that symmetry influences both band gap position and width. The study demonstrates that GA-based optimization outperforms traditional design methods. The findings indicate that higher filling rates generally produce wider band gaps. The authors conclude that structural symmetry plays a significant role in band gap formation. The study provides a framework for systematically exploring design variables in phononic crystal structures.