Advances in the design of carpet cloaks for surface elastic waves

The objective of this Ph.D. thesis pertains to the conception and design of an innovative device, called elastic carpet cloak, to protect structures from surface elastic waves, i.e. Love and Rayleigh waves. The cloak smoothly redirects surface waves around objects, without any scattering or energy loss by adjusting its material properties based on transformational elastodynamics principles. Initially, we delve into cloaking of Love waves within an isotropic layered medium. By leveraging the form invariance of the governing equation, we derive the requisite anisotropic mechanical characteristics of ideal cloaks to hide triangular and parabolic-shaped defects. We validate our approach through dispersion analyses and harmonic simulations, matching ideal cloaks with pristine mediums. Then, for triangular defects, we adapt the ideal properties into layered cloaks of monoclinic double-material unit cells, demonstrating great convergence with ideal case, as the unit cell size decreases. Next, we explore cloaking of Rayleigh waves in homogeneous mediums. By utilizing transformation elastodynamics and assuming identity gauge for the displacements, we obtain the effective cloaking properties, characterized by non-symmetric elastic tensors. To address this, we employ a symmetrization technique to approximate the non-symmetric behavior by symmetric, yet anisotropic, composites. Symmetrized cloaks with triangular and semi-circular shapes are evaluated through simulations and dispersion analyses, with a semi-circular design exhibiting superior performance. Finally, we construct 3-D cloaks for Rayleigh and Love waves, pointing out the distinctions between 3-D cloaking with the superposition of Love and Rayleigh waves and its impact on symmetrization. In particular, prismatic, and cylindrical cloaks are designed according to symmetrization method driven by the weak form solution of Love waves. Time-harmonic simulations and dispersive analyses show that a symmetrized cylindrical cloak, constructed by the "Maximal" mean, provides significant cloaking protection across all computed frequencies. This study advances the design of feasible and efficient broadband elastic cloaks for surface waves.