Harmonic Scattering of S0 Lamb Wave — A Computational Study (ISTAM 2021 Young Scientist Award Paper)

To understand and gain more insight into the interaction of the nonlinear ultrasonic S₀ guided wave and the resulting harmonic scattering from local damages, this investigation models the damage as a nonlinear elastic material while maintaining the same linear impedance as the surrounding linear elastic material. The existence of backscattered waves is shown due to the interaction of monochromatic waves and one-way two-wave mixing.

Amplitudes of harmonics are highly sensitive to the input frequencies, frequency combinations, intensity of local damages, and damage sizes. The presence and absence of backscattered higher harmonics are demonstrated by considering different case studies of harmonic scattering from local damage. Similarities of the observed harmonically scattered elastic Lamb waves are drawn by comparing with the harmonic scattering of nonlinear light waves, well known as <b>'Raman Scattering'</b> in nonlinear optics.</p><p dir="ltr"><br></p><p dir="ltr"><b>Key Contributions:</b></p><ul><li>Numerical simulation of S₀ Lamb wave interaction with localized nonlinear elastic inclusions</li><li>Demonstration of backscattered harmonic generation under single-frequency and dual-frequency one-way two-wave mixing</li><li>Sensitivity analysis of harmonic amplitudes to input frequency, frequency combination, damage intensity, and damage size</li><li>Case studies showing presence and absence of backscattered higher harmonics</li><li>Behavioral analogy between harmonically scattered elastic Lamb waves and Raman scattering in nonlinear optics</li></ul><p dir="ltr"><br></p><p dir="ltr"><b>Methodology:</b><br>A finite element method (FEM) framework is used to simulate the interaction of nonlinear ultrasonic S₀ guided waves with localized, early-stage material damage in thin plates.

The damage is modeled as a nonlinear elastic inclusion with matched linear impedance to isolate the nonlinear effects from linear scattering. Monochromatic wave excitation and one-way two-wave mixing configurations are studied across varying damage intensities and sizes. Backscattered and forward-scattered harmonic wave fields are analyzed to identify sensitivity trends and to establish the Raman scattering analogy.</p><p><br></p><p dir="ltr"><br></p><p dir="ltr"><b>Conclusions:</b></p><ul><li>Backscattered harmonic waves exist and are highly sensitive to input frequency and frequency combination</li><li>Harmonic amplitudes correlate strongly with local damage intensity and damage size</li><li>The observed behavior parallels Raman scattering in nonlinear optics</li><li>The study provides a computational baseline for nonlinear ultrasonic guided-wave damage detection in thin plate-like structures</li></ul><p dir="ltr"><br></p><p dir="ltr"><b>Award Recognition:</b> Submitted as a "Paper for the Young Scientist Award" at ISTAM 2021.</p><p dir="ltr"><br></p><p dir="ltr"><b>Published abstract (ISTAM 2021 official):</b> <a href="istam.iitkgp.ac.in/resources/2021/proceedings/Award_session/Abstract/SM/138abstract.pdf" target="_blank" rel="noreferrer">istam.iitkgp.ac.in/resources/2021/proceedings/Award_session/Abstract/SM/138abstract.pdf</a><br></p><p dir="ltr"><b>ResearchGate record:</b> <a href="researchgate.net/publication/356786945_Harmonic_Scattering_of_S0_Lamb_Wave_-_A_Computational_Study" target="_blank" rel="noreferrer">researchgate.net/publication/356786945_Harmonic_Scattering_of_S0_Lamb_Wave_-_A_Computational_Study</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><br></p><p dir="ltr"><br></p><p dir="ltr"><b>Keywords:</b> harmonic scattering, S0 Lamb wave, Lamb waves, guided waves, nonlinear ultrasonics, nonlinear elastic inclusion, one-way two-wave mixing, backscattered waves, early-stage damage, structural health monitoring, non-destructive evaluation, finite element analysis, Raman scattering analogy, ISTAM 2021, Young Scientist Award</p>