Achieving control of in-plane elastic waves

Abstract

We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves.\ud The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are\ud deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity\ud of our approach is confirmed by comparison of the analytic Green’s function in homogeneous\ud isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic\ud elastic region surrounded by perfectly matched layers

Fluid Flow Control with Transformation Media

“…The key idea that enabled progress in those areas was the combination of coordinate transformations with coordinate-dependent, and often extremely exotic [5,[13][14][15], material properties. Transformation optics [3][4][5]11,16] and transformation acoustics [6-8] offer solutions to some inverse scattering problems [17] by reducing them to an elementary one-for example, scattering off a point object in free space.There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

“…There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

Manipulating DC Currents with Bilayer Bulk Natural Materials

“…Besides making objects invisible [1][2][3][4] , many other novel devices are rapidly emerging, with a representative one being a concentrator [5,6] that can enhance the energy density of incident waves in a given area. In addition to manipulation of EM waves [1][2][3][4][5][6] , the theoretical tool of coordinate transformation has been extended to other areas of physics (such as acoustic waves [7] , matter waves [8] and elastic waves [9] ).Recently, many significant achievements have been made in the manipulation of magnetostatic field [10][11][12][13][14][15] , thermal conduction [16][17][18][19] , and electrostatic field [20][21][22][23][24] . In 2007, Wood and Pendry proposed a dc metamaterial that pointed the way towards the design of static magnetic cloak [10] , and the dc metamaterial was experimentally verified soon afterwards [11] .…”

Transformation method and wave control

“…It is seen that the derived transformed relations for material parameters have the necessary symmetry, which means that they are realizable contrary to those reported in [32]. In the following section, we will present an example to design an elastic concentrator to illustrate how to control elastic wave by the transformed relation given by Eq.…”