Harmonic Scattering of Waves from Crossed-Thin-Rectangular Nonlinear Inclusions — NODYCON 2023 Conference Paper

Harmonically scattered waves show the presence of longitudinal and transverse waves and their higher harmonics (2f, 3f) over 360° scattered angles. This understanding is used to quantify highly local early-stage damages using a nonlinear ultrasonic technique. As the number of nonlinear local damages increases, the complexity of multiple interactions of harmonically scattered waves increases, and theoretical techniques fall short of studying such problems.</p><p dir="ltr">In this study, the finite element method is used to understand the complex behavior of harmonically scattered nonlinear waves from multiple nonlinear inclusions of complex shapes.

Considering the direction and mode dependency of harmonically scattered waves, a unique shape of nonlinear inclusion is proposed — the crossed-thin-rectangular inclusion — to explore the possibilities of nonlinear wave manipulations. Nonlinear inclusions are modeled as a Murnaghan hyperelastic material. There is no impedance mismatch between the matrix material and the embedded nonlinear inclusions, isolating the nonlinear effects from linear scattering.</p><p dir="ltr"><br></p><p dir="ltr"><b>Results and Discussion:</b></p><ul><li>The interaction of the monochromatic (f = 2 MHz) longitudinal wave with the proposed shape of nonlinear inclusions shows the generation of higher harmonics (2f and 3f).</li><li>The harmonic responses of received waves at transducer T₂ show that with an increase in the number of embedded nonlinear inclusions, the amplitude of higher harmonics decreases when θ = 45°.</li><li>As the number of periodically spaced nonlinear inclusions reaches 32, the 2nd (2f) and 3rd (3f) harmonics, along with the static term (0f), vanish despite the presence of a large number of nonlinear inclusions — an <b>"elastically invisible" configuration</b>.</li><li>Due to multiple complex phenomena — harmonic scattering, mode conversion, and trapping of harmonically scattered waves in linear regions because of interference — higher harmonics cancel out as they reach the receiving end.</li><li>The change in inclination angle (θ) greatly affects the amplitude of the 3rd harmonic but is nearly insensitive to the amplitude of the 2nd harmonic.</li></ul><p dir="ltr"><br></p><p dir="ltr"><b>Conclusions:</b> Results clearly show that nonlinear waves can be manipulated by tuning parameters related to embedded nonlinear inclusions.

These computational studies will motivate researchers to design novel nonlinear metamaterials.</p><p dir="ltr"><br></p><p dir="ltr"><b>Key Contributions:</b></p><ul><li>Novel crossed-thin-rectangular inclusion geometry for nonlinear wave manipulation</li><li>Demonstration of an "elastically invisible" configuration with 32 periodically spaced inclusions</li><li>Analysis of harmonic energy exchange between longitudinal and transverse scattered waves</li><li>Insight into interference-driven cancellation of higher harmonics in nonlinear metamaterials</li></ul><p><br></p><p dir="ltr"><br></p><p dir="ltr"><b>Published abstract (NODYCON 2023 official):</b> <a href="nodycon.org/2023/papers/337/abstract_submissions/581/view_abstract" target="_blank" rel="noreferrer">nodycon.org/2023/papers/337/abstract_submissions/581/view_abstract</a><br></p><p dir="ltr"><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>Reference:</b> Kube C. M. (2017) Scattering of Harmonic Waves from a Nonlinear Elastic Inclusion.

J. Acoust. Soc. Am., 141(6): 4756–4767.</p><p dir="ltr"><br></p><p dir="ltr"><b>Keywords:</b> harmonic scattering, crossed-thin-rectangular inclusions, nonlinear inclusions, nonlinear metamaterials, Murnaghan hyperelastic material, finite element method, nonlinear wave manipulation, higher harmonics, mode conversion, elastic invisibility, NODYCON 2023, structural health monitoring</p>