Nonlinear transformation-based broadband cloaking for flexural waves in elastic thin plates

Controlling and guiding elastic waves in solids is more complicated compared with electromagnetic and acoustic waves; design and fabrication of an elastic wave cloak with non-singular, homogeneous, and isotropic material parameters is a challenging task. Recent studies in the literature that focus on manipulating flexural waves in elastic thin plates mainly use a linear transformation with a linear radial-dependent mapping function, which has drawbacks of being narrowly banded or even having negative cloaking efficiency that results from singular material parameters on the internal boundary of the cloak. This paper presents a theory of nonlinear transformation-based flexural waves and derives the nonlinear ray-tracing equation for flexural waves. A broadband cylindrical cloak for flexural waves in an elastic thin plate is realized based on a nonlinear transformation, whose materials can be simplified as layered non-singular, homogeneous, and isotropic materials using an effective medium theory. Some advantages and improvements of the invisibility nonlinear-transformation cloak are analyzed by comparison with the linear-transformation cloak. The invisibility capability of the nonlinear-transformation cloak can be tuned by adjusting an impact parameter that is shown to have influence on flexural wave energy emitting into the region inside the cloak. Numerical simulations show that the nonlinear-transformation cloak is more effective for guiding flexural waves that propagate in the region outside the cloak than the linear-transformation cloak in a broad frequency range. They also show that the nonlinear-transformation cloak can accurately control ray tracing of different types of flexural waves under disturbances outside the cloak. The methodology developed here can be used to construct nonlinear-transformation cloaks for other types of waves. (C) 2019 Elsevier Ltd. All rights reserved.