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Harmonic Scattering of Waves from Crossed-Thin-Rectangular Nonlinear Inclusions — NODYCON 2023 Conference Paper Pravinkumar Ghodake (3701242) Engineering education Mechanical engineering asset management Mechanical engineering not elsewhere classified Applications in physical sciences Other physical sciences not elsewhere classified Acoustics and noise control (excl. architectural acoustics) Acoustics and acoustical devices; waves Solid mechanics Theoretical and applied mechanics Computational complexity and computability Computational modelling and simulation in earth sciences Numerical and computational mathematics not elsewhere classified Data visualisation and computational (incl. parametric and generative) design Numerical modelling and mechanical characterisation Nonlinear optics and spectroscopy Numerical analysis Numerical computation and mathematical software Numerical solution of differential and integral equations Engineering design Computer aided design Design practice and methods Industrial and product design Design not elsewhere classified Design history, theory and criticism Models and simulations of design Theory and design of materials NODYCON 2023 Harmonic Scattering harmonic scattering Harmonic Scattering Angle-resolved harmonic scattering intensities crossed-thin-rectangular inclusions nonlinear inclusions nonlinear metamaterials Nonlinear Metamaterials Murnaghan hyperelastic material finite element method nonlinear wave manipulation higher harmonics mode conversion elastic invisibility elastically invisible inclusions second harmonic suppression third harmonic suppression static term cancellation harmonic energy exchange longitudinal waves Longitudinal waves transverse waves wave interference Wave Interference wave interference phenomenon Energy Trapping Energy Trapping Luminescence efficiency early-stage damage structural health monitoring Structural Health Monitoring (SHM). Structural Health Monitoring Sensors Structural health monitoring systems Structural health monitoring. Structural Health Monitoring (SHM) structural health monitoring (SHM) Structural health monitoring (SHM) Structural Health Monitoring STRUCTURAL HEALTH MONITORING Structural health monitoring Structural health monitoring Aircraft availability non-destructive evaluation non-destructive evaluation inspection Non-destructive evaluation (NDE) Non-Destructive Evaluation (NDE) Non-destructive Evaluation Non-Destructive Evaluation Non-destructive evaluation solid mechanics solid mechanics problems Solid mechanics and dynamics Solid mechanics Solid Mechanics Pravinkumar Ghodake Pravinkumar Ramchandra Ghodake Design Optimization Design & technology Design & Technology Generative design research Elastodynamics simulations This conference contribution is a research paper presented by Pravinkumar Ghodake (Department of Mechanical Engineering, IIT Bombay) at NODYCON 2023 — the Third International Nonlinear Dynamics Conference. The work was submitted and published as a conference proceeding under the NODYCON Open Repository. Title of contribution: "Harmonic Scattering of Waves from Crossed-Thin-Rectangular Nonlinear Inclusions" Abstract: Nonlinear wave manipulations, like the presence and absence of higher harmonics and mode conversions due to harmonic scattering of nonlinear waves from uniquely proposed nonlinear inclusions, are demonstrated in this study using the finite element method, due to the limitations of theoretical techniques. The sensitivity of the parameters that control the shape and distribution of nonlinear inclusions is explored to capture possible overall nonlinear effects due to complex harmonic scattering and interference of scattered waves. The exchange of harmonic energies between harmonically scattered longitudinal and transverse waves from multiple nonlinear inclusions is demonstrated. This study will help researchers to design nonlinear metamaterials to control nonlinear waves, as harmonic scattering manipulates nonlinear waves effectively. Introduction: Interaction of monochromatic (f) longitudinal waves with the local single nonlinear inclusion, modeled as quadratic and cubic nonlinear material, results in harmonic scattering of the nonlinear waves; the theoretical solution was obtained by Kube (2017) using Green's functions. 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.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. Results and Discussion:<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 "elastically invisible" configuration.</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> Conclusions: 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. Key Contributions:<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> Published abstract (NODYCON 2023 official): <a href="https://nodycon.org/2023/papers/337/abstract_submissions/581/view_abstract" target="_blank" rel="noreferrer">https://nodycon.org/2023/papers/337/abstract_submissions/581/view_abstract</a> Research portfolio: <a href="https://sites.google.com/view/pravinkumarghodake/research" target="_blank" rel="noreferrer">https://sites.google.com/view/pravinkumarghodake/research</a>Reference: Kube C. M. (2017) Scattering of Harmonic Waves from a Nonlinear Elastic Inclusion. J. Acoust. Soc. Am., 141(6): 4756–4767. Keywords: 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 2026-09-30T04:08:45Z Text Conference contribution 10.6084/m9.figshare.34029327.v1 https://figshare.com/articles/conference_contribution/Harmonic_Scattering_of_Waves_from_Crossed-Thin-Rectangular_Nonlinear_Inclusions_NODYCON_2023_Conference_Paper/34029327 CC BY 4.0