scholarly journals Cloaking In-Plane Elastic Waves with Swiss Rolls

Materials ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 449 ◽  
Author(s):  
Younes Achaoui ◽  
André Diatta ◽  
Muamer Kadic ◽  
Sébastien Guenneau
Keyword(s):  
Elastic Waves ◽  
Shear Waves ◽  
Effective Medium ◽  
Scaling Factor ◽  
Displacement Fields ◽  
Plane Shear ◽  
Close Proximity ◽  
Original Medium ◽  
Cosserat Media ◽  
Sub Wavelength

We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions’ sizes is according to Pendry’s transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields u in original medium and u ′ in transformed medium remain unaffected ( u ′ = u ). This breaks the minor symmetries of the rank-4 and rank-3 tensors in the Willis equation that describe the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located in close proximity to a clamped obstacle surrounded by the structured cloak. The structured medium approximating the effective medium allows for strong Willis coupling, notwithstanding potential chiral elastic effects, and thus mitigates roles of Willis and Cosserat media in the achieved elastodynamic cloaking.

Controlling Out-of-Plane Shear Wave Propagation With Broadband Cloaking

2019 ◽  
Author(s):  
Mao Liu ◽  
W. D. Zhu
Keyword(s):  
Linear Transformation ◽  
Elastic Waves ◽  
Shear Waves ◽  
Nonlinear Transformation ◽  
Plane Shear ◽  
Shear Moduli ◽  
Transformation Medium ◽  
Invisibility Cloak ◽  
Independent Functions ◽  
Out Of Plane

Abstract A major challenge in designing a perfect invisibility cloak for elastic waves is that density and elasticity tensors need to be independent functions of its radius with a linear transformation medium. The traditional cloak for out-of-plane shear waves in membranes exhibits material properties with inhomogeneous and anisotropic shear moduli and densities, which yields a poor or even negative cloaking efficiency. This paper presents design of a cylindrical cloak for shear waves based on a nonlinear transformation. This excellent broadband nonlinear cloak only requires variation of its shear modulus, while the density in the cloak region remains unchanged. The nonlinear ray trajectory equation for out-of-plane shear waves is derived and a parameter to adjust the efficiency of the cylindrical cloak is introduced. Qualities of the nonlinear invisibility cloak are discussed by comparison with those of a cloak with the linear transformation. Numerical examples show that the nonlinear cloak is more effective for shielding out-of-plane shear waves from outside the cloak than the linear cloak and illustrate that the nonlinear cloak for shear waves remains highly efficient in a broad frequency range. The proposed nonlinear transformation in conjunction with ray trajectory equations can also be used to design nonlinear cloaks for other elastic waves.

Elastic Waves in the Half-space of an Incompressible Thermoelastic Material with Transverse Isotropy

2020 ◽  
Vol 8 (1) ◽  
pp. 58-62
Author(s):  
C. Zorammuana ◽  
◽  
Lalawmpuia Tochhawng ◽  
S.S. Singh ◽  
◽  
...  
Keyword(s):  
Free Surface ◽  
Elastic Waves ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Amplitude Ratios ◽  
Plane Shear ◽  
Reflected Waves ◽  
Thermoelastic Material

This paper investigates the problem of incident and reflected shear waves in an incompressible thermoelastic material having transversely isotropic property using Lord-Shulman theory on generalized thermoelasticity. Two plane shear waves are shown to exist in such medium and the expressions for non-dimensional velocities are given. The amplitude ratios of the reflected waves caused by the incident wave at the stress free surface have been derived by taking suitable boundary conditions. The effect of specific heat and material constants on the amplitude ratios has been analysed numerically and the results are presented graphically.

Controlling Out-of-Plane Elastic Shear Wave Propagation With Broadband Cloaking

2018 ◽  
Vol 85 (8) ◽  
Author(s):  
M. Liu ◽  
W. D. Zhu
Keyword(s):  
Linear Transformation ◽  
Elastic Waves ◽  
Shear Waves ◽  
Nonlinear Transformation ◽  
Plane Shear ◽  
Invisibility Cloak ◽  
Independent Functions ◽  
Out Of Plane ◽  
Trajectory Equation ◽  
Elastic Shear

A major challenge in designing a perfect invisibility cloak for elastic waves is that the mass density and elasticity tensor need to be independent functions of its radius with a linear transformation medium. The traditional cloak for out-of-plane shear waves in elastic membranes exhibits material properties with inhomogeneous and anisotropic shear moduli and densities, which yields a poor or even negative cloaking efficiency. This paper presents the design of a cylindrical cloak for elastic shear waves based on a nonlinear transformation. This excellent broadband nonlinear cloak only requires variation of its shear modulus, while the density in the cloak region remains unchanged. A nonlinear ray trajectory equation for out-of-plane shear waves is derived and a parameter to adjust the efficiency of the cylindrical cloak is introduced. Qualities of the nonlinear invisibility cloak are discussed by comparison with those of a cloak with the linear transformation. Numerical examples show that the nonlinear cloak is more effective for shielding out-of-plane elastic shear waves from outside the cloak than the linear cloak and illustrate that the nonlinear cloak for shear waves remains highly efficient in a broad frequency range. The proposed nonlinear transformation in conjunction with the ray trajectory equation can also be used to design nonlinear cloaks for other elastic waves.

Transverse surface waves in magneto-elasticity

1966 ◽  
Vol 62 (3) ◽  
pp. 541-545 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Waves ◽  
Elastic Medium ◽  
Uniform Magnetic Field ◽  
Shear Waves ◽  
Plane Shear ◽  
Electrically Conducting ◽  
Velocity Of Propagation

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

An effective medium model for elastic waves in microcrack damaged media

2008 ◽  
Vol 75 (14) ◽  
pp. 4104-4116 ◽  
Author(s):  
Dan Su ◽  
Michael H. Santare ◽  
George A. Gazonas
Keyword(s):  
Elastic Waves ◽  
Effective Medium ◽  
Effective Medium Model ◽  
Medium Model

Inelastic behaviour of grain skeletons with propagation of plane shear waves

2020 ◽  
pp. 125-128
Author(s):  
Gerd Gudehus ◽  
Iouri Loukachev ◽  
Norbert Pralle
Keyword(s):  
Shear Waves ◽  
Plane Shear ◽  
Inelastic Behaviour

scholarly journals Interferometric imaging of nonlocal electromechanical power transduction in ferroelectric domains

2018 ◽  
Vol 115 (21) ◽  
pp. 5338-5342 ◽  
Author(s):  
Lu Zheng ◽  
Hui Dong ◽  
Xiaoyu Wu ◽  
Yen-Lin Huang ◽  
Wenbo Wang ◽  
...  
Keyword(s):  
Electric Fields ◽  
Elastic Waves ◽  
Near Field ◽  
Nanoelectromechanical Systems ◽  
Nonlocal Interaction ◽  
Interferometric Imaging ◽  
Displacement Fields ◽  
Domain Structures ◽  
Acoustic Wave Devices ◽  
Electrical Generation

The electrical generation and detection of elastic waves are the foundation for acoustoelectronic and acoustooptic systems. For surface acoustic wave devices, microelectromechanical/nanoelectromechanical systems, and phononic crystals, tailoring the spatial variation of material properties such as piezoelectric and elastic tensors may bring significant improvements to the system performance. Due to the much slower speed of sound than speed of light in solids, it is desirable to study various electroacoustic behaviors at the mesoscopic length scale. In this work, we demonstrate the interferometric imaging of electromechanical power transduction in ferroelectric lithium niobate domain structures by microwave impedance microscopy. In sharp contrast to the traditional standing-wave patterns caused by the superposition of counterpropagating waves, the constructive and destructive fringes in microwave dissipation images exhibit an intriguing one-wavelength periodicity. We show that such unusual interference patterns, which are fundamentally different from the acoustic displacement fields, stem from the nonlocal interaction between electric fields and elastic waves. The results are corroborated by numerical simulations taking into account the sign reversal of piezoelectric tensor in oppositely polarized domains. Our work paves ways to probe nanoscale electroacoustic phenomena in complex structures by near-field electromagnetic imaging.

scholarly journals Steering in-plane shear waves with inertial resonators in platonic crystals

2015 ◽  
Vol 106 (22) ◽  
pp. 223502 ◽  
Author(s):  
Younes Achaoui ◽  
André Diatta ◽  
Sébastien Guenneau
Keyword(s):  
Shear Waves ◽  
Plane Shear
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