Related papers: Transformation elastodynamics and cloaking for fle…
It is known that design of elastic cloaks is much more challenging than the design idea for acoustic cloaks, cloaks of electromagnetic waves or scalar problems of anti-plane shear. In this paper, we address fully the fourth-order problem…
We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to…
The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the…
This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we…
Cloaking elastic waves has, in contrast to the cloaking of electromagnetic waves, remained a fundamental challenge: the latter successfully uses the invariance of Maxwell's equations, from which the field of transformational optics has…
We present a new method to create an active cloak for a rigid inclusion in a thin plate, and analyse flexural waves within such a plate governed by the Kirchhoff plate equation. We consider scattering of both a plane wave and a cylindrical…
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics.
In this paper, we bring to the awareness of the scientific community and civil engineers, an important fact: the possible lack of wave protection of transformational elastic cloaks. To do so, we propose spherical cloaks described by a…
In this paper we formulate the problem of elastodynamic transformation cloaking for Kirchhoff-Love plates and elastic plates with both the in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value problem of…
Love waves are antiplane elastic waves which propagate along the surface of a heterogeneous medium. Under time-harmonic regime, they are governed by a scalar equation of the Helmholtz type. We exploit the invariance of this governing…
In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking…
Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric…
Transformation media theory, which steers waves in solids via an effective geometry induced by a refractive material (Fermat's principle of least action), provides a means of controlling vibrations and elastic waves beyond the traditional…
Transformation elasticity, by analogy with transformation acoustics and optics, converts material domains without altering wave properties, thereby enabling cloaking and related effects. By noting the similarity between transformation…
In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lam\'e system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first…
Steering waves in elastic solids is more demanding than steering waves in electromagnetism or acoustics. As a result, designing material distributions which are the counterpart of optical invisibility cloaks in elasticity poses a major…
A perturbation approach is used for analysis of a near-cloak in shielding a finite scatterer from an incident flexural wave. The effect of the boundary conditions on the interior surface of the cloaking layer is analysed in detail, based on…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate…
A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows…