Shape optimization of phononic band gap structures using the homogenization approach

摘要: Abstract The paper deals with optimization of the acoustic band gaps computed using homogenized model strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff matrix. We employ such medium to compute intervals — incident wave frequencies for waves cannot propagate. It was demonstrated that distribution can be influenced changing shape inclusions. Therefore, we deal problem maximize low-frequency gaps; their bounds are determined analysing effective mass tensor medium. Analytic transformation formulas derived describe dispersion effects resizing core lies sensitivity eigenvalue associated microstructure. Computational analysis developed, allows efficient usage gradient based methods. Numerical examples 2D structures reported illustrate stiffness constraint. This study aimed develop modelling tools used optimal design new devices “smart systems”.