Abstract
A gradient-based optimization (GBO) method is presented for acoustic lens design and sound localization. GBO uses a semi-analytical optimization combined with the principle of acoustic reciprocity. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. We first derive a formula for the gradients of the pressure at the focal point with respect to positions of a set of cylindrical scatterers. The analytic form of the gradients enhances modeling capability when combined with optimization algorithms and parallel computing. The GBO algorithm maximizes the sound amplification at the focal point and enhances the sound localization by evaluating pressure derivatives with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while incorporating multiple scattering between the cylindrical scatterers. The results of the GBO of the uni- and multi-directional broadband acoustic lens designs are presented including several performance measures for the frequency dependence and the incidence angle. A multi-directional broadband acoustic lens is designed to localize the sound and to focus acoustic incident waves received from multiple directions onto a predetermined localization region or focal point. The method is illustrated for configurations of sound hard and sound soft cylinders as well as clusters of elastic thin shells in water.
Highlights
Metamaterials are engineered materials that can control and guide the energy flow with capabilities exceeding those possible in conventional materials, enabling the control of acoustic, electromagnetic, and mechanical waves
Computations are performed on MATLAB using advanced parallel optimization algorithms, the MultiStart optimization solver combined with fmincon solver and sequential quadratic programming (SQP) algorithms, and supplying the gradients of absolute pressure amplitude at the focal point | p f |
We have demonstrated that the gradient-based optimization (GBO) technique combined with the principle of acoustic reciprocity leads to an effective method to optimally arrange scatterers so as to produce acoustic focusing
Summary
Metamaterials are engineered materials that can control and guide the energy flow with capabilities exceeding those possible in conventional materials, enabling the control of acoustic, electromagnetic, and mechanical waves. We obtain a semi-analytical formula for the gradient of the pressure at the focal point with respect to positions of a set of cylindrical scatterers using two approaches namely forward and reciprocal formulations. We combine these formulae with GBO algorithms and apply them to design a uni- and multi-incidence-directional broadband lens by means of multiple scattering theory and applying the principle of reciprocity. Gradients of the absolute acoustic pressure at the focal point with respect to cylinder positions are obtained by means of multiple scattering theory for forward and reciprocal formulations. Single and broadband as well as uni- and multi-directional focusing effects are illustrated using multiple reconfigurable cylinders as the lensing and localization mechanisms
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