Shape Optimization for the Design of Linear and Nonlinear Metamaterials to Improve Nonlinear Ultrasonic Testing — NDE 2021 Conference Talk [Video Presentation]

During the design of such phononic devices, calculation of the optimal geometric parameters — such as the thickness of individual layers of different materials and the total thickness of the phononic device — is challenging and time-consuming due to large sets of parametric sweeps.</p><p dir="ltr">In this study, a shape optimization problem is defined for the design of linear and nonlinear phononic devices to stop a wide range of higher harmonics.

Steel and glass are selected due to their possible bandgap structure. The shape optimization problem is solved using non-gradient algorithms with the main objective of reducing amplitudes of the higher harmonics (2f, 3f, and 4f). Even though the amplitudes of the higher harmonics (3f, 4f) are lower, as we try to stop energy corresponding to 2f after optimization, the phononic device might divert this energy to other harmonics such as 1.5f, 2.5f, 3f, 3.5f, and 4f.

The linear and nonlinear wave propagation problems are solved using COMSOL finite element software, and the optimization loop is added by integrating MATLAB and COMSOL. The stopping of the higher harmonics is demonstrated after using the obtained optimal solution of the shape optimization problems. The process of solving the forward finite element problem and then solving an inverse problem of finding the optimal layer thicknesses — by applying weak constraints on the total thickness of the metamaterial lattice — is fully automated.

Various computational studies are carried out to demonstrate the applicability of the proposed approach for the design of linear and nonlinear metamaterials. In some cases, the design of linear metamaterials is sufficient, as the same can be used as a nonlinear metamaterial. Complete flexibility in the optimization can be added by optimizing all three variables: the thickness of steel and glass in a periodic structure, and the final thickness of the metamaterial based on the number of repeated periodic structures.</p><p dir="ltr"><br></p><p dir="ltr"><b>Talk outline / timestamps:</b><br>0:00 Introduction to Nonlinear Ultrasonic Testing and Parasitic System Harmonics<br>2:15 Motivation: Masking Effects Caused by Instrumentation, Transducers, and Couplants<br>4:30 Phononic Bandgaps and Layered Metamaterial Design Principles<br>6:45 Formulation of the Shape Optimization Problem for Linear and Nonlinear Devices<br>9:10 Numerical Implementation: Coupling MATLAB and COMSOL for Automated Optimization<br>11:35 Results: Harmonic Suppression (2f, 3f, 4f) and Optimal Steel-Glass Layer Thicknesses<br>13:50 Conclusion and Summary of Applicability in NDE</p><p><br></p><p dir="ltr"><b>Video:</b> <a href="youtu.be/PyJpewnetOQ" target="_blank" rel="noreferrer">youtu.be/PyJpewnetOQ</a><br></p><p dir="ltr"><b>Published article (</b><a href="ndt.net/" target="_blank" rel="noreferrer"><b>NDT.net</b></a><b> / eJNDT):</b> <a href="ndt.net/search/docs.php?id=26801" target="_blank" rel="noreferrer">ndt.net/search/docs.php?id=26801</a><br></p><p dir="ltr"><b>Research portfolio:</b> <a href="sites.google.com/view/pravinkumarghodake/research" target="_blank" rel="noreferrer">sites.google.com/view/pravinkumarghodake/research</a></p><p dir="ltr"><b>Note:</b> This is a 14 min 37 sec conference presentation summarizing peer-reviewed research published in the e-Journal of Nondestructive Testing (eJNDT), linking advanced optimization techniques with structural wave mechanics.</p><p dir="ltr"><br></p><p dir="ltr"><b>Keywords:</b> shape optimization, nonlinear ultrasonics, linear metamaterials, nonlinear metamaterials, harmonic scattering, phononic crystals, bandgap, finite element analysis, COMSOL, MATLAB, non-gradient optimization, ultrasonic testing, NDE 2021, ISNDT, eJNDT, structural health monitoring</p>