Abstract
Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. The primary advantage of our square lattice cloak, over other designs, is the straightforward implementation and the ease of construction. The elastic lattice cloak, implemented experimentally, shows high efficiency.
Highlights
Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice
One cannot create an invisibility cloak for elastodynamics without recourse to a non-classical generalised theory of elasticity, Norris & Shuvalov[7] later extended the framework of Milton et al.[5,6] and showed that, with an appropriate choice of Gauge, one can choose between creating a micropolar elastic cloak or a cloak with tensorial density, for example
The concept, design, and theoretical analysis of elastodynamic invisibility cloaks are much more challenging compared to cloaks for membrane, acoustic, optical, and anti-plane shear waves, all of which are governed by the transformed Helmholtz equation
Summary
In most of the papers addressing the design of cloaks for linear waves, a singular radially symmetric push-out transformation is employed (see, for example13,34) which maps a point to a finite disc. As shown recently[11], the correct choice of boundary condition is of vital importance in order to achieve cloaking, and in particular, replacement of the Neumann boundary condition with the Dirichlet condition, corresponding to a clamped boundary, would not be a feasible choice for cloaking of flexural waves in the Kirchhoff plate This observation answers a related question “Is the regularised cloak better than an imperfectly fabricated singular cloak”. The thin elastic ligaments may be treated as beams of rectangular cross section characterised by the bending stiffnesses D1 and D2 chosen in accordance with the analytical formulae from[2] Equations (5), together with the accompanying geometrical design of the cloak, provide the essential information for the experimental implementation discussed above
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