<p>Precise control of longitudinal and transverse elastic wave modes in compact, subwavelength metamaterials remains challenging, especially for arbitrary oblique incidence and across different media. Existing topology optimization methods are confined to normal incidence in the same media and to wavelength-scale layers, limiting their practical relevance. We propose a generalized density-based topology optimization framework enabling near-perfect conversion and preservation between longitudinal (L) and transverse (T) wave modes for single or broadband frequencies at any incident angle. The method combines a gradient-based optimizer with density filter, <i>S</i>-shaped mapping function, exact analytical transmittance expressions, and newly derived closed-form sensitivities within a finite element model. The optimizer ensures convergence within tens of iterations. Demonstrations include L-to-T mode conversion at large oblique angles with over 99% efficiency, and L-to-L mode-preserving, both in different media. The framework supports subwavelength-scale unit cells as small as one-eighth of the longitudinal wavelength, enabling extremely compact designs. Divergence and curl fields of displacement confirm nearly perfect transmission without parasitic wave modes, precisely at propagation angles predicted by Snell’s law. Additionally, reciprocity verifies physical validity. The proposed approach provides a powerful, automated design tool for elastic wave problems including mode-conversion or mode-preserving. It has applications in ultrasonic flowmeters, structural health monitoring, non-destructive testing, and medical ultrasound imaging, where conventional designs are deficient.</p>

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Topology optimization of subwavelength elastic metamaterials for arbitrary-angle mode conversion and preservation

  • Tam Yee Ha,
  • Yoon Young Kim,
  • Gil Ho Yoon

摘要

Precise control of longitudinal and transverse elastic wave modes in compact, subwavelength metamaterials remains challenging, especially for arbitrary oblique incidence and across different media. Existing topology optimization methods are confined to normal incidence in the same media and to wavelength-scale layers, limiting their practical relevance. We propose a generalized density-based topology optimization framework enabling near-perfect conversion and preservation between longitudinal (L) and transverse (T) wave modes for single or broadband frequencies at any incident angle. The method combines a gradient-based optimizer with density filter, S-shaped mapping function, exact analytical transmittance expressions, and newly derived closed-form sensitivities within a finite element model. The optimizer ensures convergence within tens of iterations. Demonstrations include L-to-T mode conversion at large oblique angles with over 99% efficiency, and L-to-L mode-preserving, both in different media. The framework supports subwavelength-scale unit cells as small as one-eighth of the longitudinal wavelength, enabling extremely compact designs. Divergence and curl fields of displacement confirm nearly perfect transmission without parasitic wave modes, precisely at propagation angles predicted by Snell’s law. Additionally, reciprocity verifies physical validity. The proposed approach provides a powerful, automated design tool for elastic wave problems including mode-conversion or mode-preserving. It has applications in ultrasonic flowmeters, structural health monitoring, non-destructive testing, and medical ultrasound imaging, where conventional designs are deficient.