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Madine KH, Colquitt DJ. Negative refraction and mode trapping of flexural-torsional waves in elastic lattices. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210379. [PMID: 36209800 PMCID: PMC9548396 DOI: 10.1098/rsta.2021.0379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 05/04/2022] [Indexed: 06/16/2023]
Abstract
We consider the propagation of flexural and torsional waves in a square lattice of Euler-Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
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Affiliation(s)
- K. H. Madine
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
- Department of Materials Engineering, National Tsing Hua University, Hsinchu City, Taiwan
- IPHD Programme, National Tsing Hua University, Hsinchu City, Taiwan
| | - D. J. Colquitt
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
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Hima N, Bigoni D, Dal Corso F. Buckling versus unilateral constraint for a multistable metamaterial element. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20220021. [PMID: 35858080 DOI: 10.1098/rsta.2022.0021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 04/03/2022] [Indexed: 06/15/2023]
Abstract
A structural element is designed and investigated, forming the basis for the development of an elastic multistable metamaterial. The leitmotif of the structural design is the implementation of a strut characterized by a bifurcation occurring at either vanishing tensile or compressive load. It is shown that buckling at null load leads to a mechanical equivalence with a unilateral constraint formulation, introducing shocks in dynamics. Towards a future analysis of the latter, the nonlinear quasi-static response is investigated, showing the multistable character of the structure, which may appear as bistable or tetrastable. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
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Affiliation(s)
- N Hima
- DICAM, University of Trento, via Mesiano 77, Trento 38123, Italy
- FIP MEC srl, via Scapacchiò 41, Selvazzano Dentro PD 35030, Italy
| | - D Bigoni
- DICAM, University of Trento, via Mesiano 77, Trento 38123, Italy
| | - F Dal Corso
- DICAM, University of Trento, via Mesiano 77, Trento 38123, Italy
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Xu X, Wang C, Shou W, Du Z, Chen Y, Li B, Matusik W, Hussein N, Huang G. Physical Realization of Elastic Cloaking with a Polar Material. PHYSICAL REVIEW LETTERS 2020; 124:114301. [PMID: 32242717 DOI: 10.1103/physrevlett.124.114301] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 03/04/2020] [Indexed: 06/11/2023]
Abstract
An elastic cloak is a coating material that can be applied to an arbitrary inclusion to make it indistinguishable from the background medium. Cloaking against elastic disturbances, in particular, has been demonstrated using several designs and gauges. None, however, tolerate the coexistence of normal and shear stresses due to a shortage of physical realization of transformation-invariant elastic materials. Here, we overcome this limitation to design and fabricate a new class of polar materials with a distribution of body torque that exhibits asymmetric stresses. A static cloak for full two-dimensional elasticity is thus constructed based on the transformation method. The proposed cloak is made of a functionally graded multilayered lattice embedded in an isotropic continuum background. While one layer is tailored to produce a target elastic behavior, the other layers impose a set of kinematic constraints equivalent to a distribution of body torque that breaks the stress symmetry. Experimental testing under static compressive and shear loads demonstrates encouraging cloaking performance in good agreement with our theoretical prediction. The work sets a precedent in the field of transformation elasticity and should find applications in mechanical stress shielding and stealth technologies.
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Affiliation(s)
- Xianchen Xu
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
| | - Chen Wang
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
| | - Wan Shou
- Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zongliang Du
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
- Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, People's Republic of China
| | - Yangyang Chen
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
| | - Beichen Li
- Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wojciech Matusik
- Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nassar Hussein
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
| | - Guoliang Huang
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
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