scholarly journals Steering Flexural Waves by Amplitude-Shift Elastic Metasurfaces

2021 ◽  
pp. 1-36
Author(s):  
Guangyuan Su ◽  
Yunhao Zhang ◽  
Yongquan Liu ◽  
T.J. Wang
Keyword(s):  
Elastic Waves ◽  
Theoretical Calculations ◽  
Experimental Tests ◽  
Cylindrical Wave ◽  
Thin Plates ◽  
Flexural Waves ◽  
Complete Control ◽  
Additional Degree ◽  
Artificial Boundary Conditions ◽  
Incident Waves

Abstract As 2D materials with subwavelength thicknesses, elastic metasurfaces show remarkable abilities to manipulate elastic waves at will through artificial boundary conditions. However, current elastic metasurfaces are still far away from arbitrary wave manipulations since they just play a role of phase compensator. Herein, we present the next generation of elastic metasurfaces by incorporating amplitude discontinuities as an additional degree of freedom. A general theory predicting target wave fields steered by metasurfaces is proposed by modifying the Huygens-Fresnel principle. As examples, two amplitude-shift metasurfaces concerning flexural waves in thin plates are carried out: one is to transform a cylindrical wave into a Gaussian beam by elaborating both amplitude and phase shifts, and the other one is to focus incident waves by metasurfaces of amplitude modulations only. These examples coincide well over theoretical calculations, numerical simulations, and experimental tests. This work may underlie the design of metasurfaces with complete control over guided elastic waves, and may extend to more sophisticated applications, such as analog signal processing and holographic imaging.

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

scholarly journals Numerical Assessment of the Performance of Elastic Cloaks for Transient Flexural Waves

2020 ◽  
Vol 7 ◽  
Author(s):  
Marco Rossi ◽  
Daniele Veber ◽  
Massimiliano Gei
Keyword(s):  
Finite Element ◽  
Thin Plates ◽  
Winkler Foundation ◽  
Finite Element Code ◽  
Flexural Waves ◽  
Transient Waves ◽  
Mathematical Transformation ◽  
Plane Body ◽  
Numerical Assessment ◽  
Subgrade Modulus

A relevant application of transformation elastodynamics has shown that flexural waves in a Kirchhoff-Love plate can be diverted and channeled to cloak a region of the ambient space. To achieve the goal, an orthotropic meta-structural plate should be employed. However, the corresponding mathematical transformation leads to the presence of an unwanted strong compressive prestress, likely beyond the buckling threshold of the structure, with a set of in-plane body forces to warrant equilibrium. In addition, the plate must possess, at the same time, high bending stiffnesses, but a null twisting rigidity. With the aim of estimating the performance of cloaks modelled with approximate parameters, an in-house finite element code, based on a subparametric technique, is implemented to deal with the cloaking of transient waves in orthotropic thin plates. The tool allows us to explore the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. In addition, the finite element code is extended to investigate a meta-plate interacting with a Winkler foundation, to confirm how the subgrade modulus should transform in the cloak region.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

Wave-Induced Hull Vibrations: An Experimental and Theoretical Study

1984 ◽  
Vol 28 (02) ◽  
pp. 141-150
Author(s):  
Armin W. Troesch
Keyword(s):  
Great Lakes ◽  
Short Wavelength ◽  
Theoretical Study ◽  
Theoretical Calculations ◽  
Hull Girder ◽  
Bulk Carriers ◽  
Wave Induced ◽  
Incident Waves

The results of an experimental and theoretical study investigating the main hull girder vibrations of Great Lakes bulk carriers are presented. The source of the excitation is considered to be the incident waves. The emphasis of the work is to understand the hydrodynamic aspects of ship springing. Theoretical calculations based upon a short-wavelength assumption compare well with experiments.

scholarly journals Poisson-like effect for flexural waves in periodically perforated thin plates

2018 ◽  
Vol 144 (2) ◽  
pp. 1053-1058 ◽  
Author(s):  
Penglin Gao ◽  
José Sánchez-Dehesa ◽  
Linzhi Wu
Keyword(s):  
Thin Plates ◽  
Flexural Waves

Accuracy of Green's function estimation from correlation of diffuse elastic waves on thin plates

2019 ◽  
Vol 146 (5) ◽  
pp. 3505-3511
Author(s):  
Lynda Chehami ◽  
Emmanuel Moulin ◽  
Julien de Rosny ◽  
Claire Prada
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Waves ◽  
Thin Plates ◽  
Function Estimation

scholarly journals Experiments on cloaking in optics, thermodynamics and mechanics

2015 ◽  
Vol 373 (2049) ◽  
pp. 20140357 ◽  
Author(s):  
Muamer Kadic ◽  
Tiemo Bückmann ◽  
Robert Schittny ◽  
Martin Wegener
Keyword(s):  
Three Dimensional ◽  
Thin Plates ◽  
Visible Range ◽  
Flexural Waves ◽  
Discrete Lattices ◽  
Mechanical Metamaterials ◽  
Visible Frequency ◽  
Transient Thermal ◽  
Thermal Cloaking ◽  
Static Core

Spatial coordinate transformations can be used to transform boundaries, material parameters or discrete lattices. We discuss fundamental constraints in regard to cloaking and review our corresponding experiments in optics, thermodynamics and mechanics. For example, we emphasize three-dimensional broadband visible-frequency carpet cloaking, transient thermal cloaking, three-dimensional omnidirectional macroscopic broadband cloaking for diffuse light throughout the entire visible range, cloaking for flexural waves in thin plates and three-dimensional elasto-static core–shell cloaking using pentamode mechanical metamaterials.

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