Metamaterials are engineered  materials that can manipulate the energy flow with capabilities exceeding those possible in conventional materials, enabling the control of acoustic, electromagnetic, and mechanical waves. Despite the exciting results obtained by the physics-inspired metamaterial designs, the forward design methodology relies on tuning parameters by trial and error where the low efficiency and limited exploration of the design variations tend to omit the optimal solution. Using the inverse design approaches, one can start from the opposite end and optimize certain objective functions describing the desired functionality. The progress in inverse design has led to the discovery of metastructures with  
exceptional performances. Among various methods, large-scale gradient-based optimization  
has been a popular approach to design structures containing a vast number of degrees of freedom.

In this work, we present a  gradient-based optimization method for the design of acoustic lens. This design is based on an optimization process using the semi-analytical optimization approach and applying the principle of reciprocity. Acoustic reciprocity is well known. The acoustic pressure at position *x~i ~* due to a monopole source at position *x~f ~* is identical to the pressure at *x~f ~* resulting from a monopole of the same strength located at *x~i ~*.  Here, we will illustrate the use of acoustic reciprocity to define the pressure at the focal point *P~f ~* due to a source located in a far-field. The reciprocity enables us to relate the response by configuration of scatterers for an incident plane wave in terms of the far-field Green’s function. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms.  The gradient-based optimization algorithm maximizes the sound amplification at the focal point by evaluating pressure derivative with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while taking into account acoustic the multiple scattering between the cylinders. Computations are performed on MATLAB using MATLAB built *fmincon  *function with sequential quadratic programming  algorithms, and with a *MultiStart* optimization solver, and supplying the gradient of pressure at the focus. We consider two problem formulations, namely forward and reciprocal, and make comparison of simulation times for both formulations. The reciprocal formulation of inverse design of acoustic lens leads to the closed form solution that takes lesser time to compute the absolute pressure and it gradients at focal point. The results of the gradient-based optimization of the uni- and multi-directional broadband acoustic lens designs are presented including several performance measures for the frequency dependence and the incidence angle. The real part of computed total pressure fields show clearly the focusing effect; the plane incident wave falling from left to right is focused on the side of the lens resembling the acoustic Luneburg lens effect.

 


Broadband Uni- and Multi-Directional Acousticlens Design Using Gradient-Based Optimization

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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