相关论文: Transformation Cloaking in Elastic Plates
We formulate the problems of nonlinear and linear elastodynamics transformation cloaking in a geometric framework. It is noted that a cloaking transformation is neither a spatial nor a referential change of frame (coordinates); a cloaking…
We propose an alternative approach called backward transformation for the design of platonic cloaks, without resorting to in-plane body forces and pre-stresses, which can lead to unphysical features. It is shown that the Kirchhoff-Love…
The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general…
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…
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…
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This…
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…
In this paper we investigate the possibility of elastodynamic transformation cloaking in bodies made of non-centrosymmetric gradient solids. The goal of transformation cloaking is to hide a hole from elastic disturbances in the sense that…
We consider the two-dimensional Kirchhoff-Love plate equation in the context of elasticity modeling the stresses and deformations in thin plates subjected to forces and moments. We establish global recovery of the material parameters like…
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material…
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 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…
In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…
The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional…
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…
In [AIP Advances 6, 121707 (2016)], a soil structured with concrete columns distributed within two specially designed seismic cloaks thanks to a combination of transformational elastodynamics and effective medium theory was shown to detour…
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 address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…
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…
The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics, and reconfigurable microfluidic devices. In this work we examine non-uniform…