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

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.

Download Full-text

Acoustical wave propagator for time-domain flexural waves in thin plates

The Journal of the Acoustical Society of America ◽

10.1121/1.1639905 ◽

2004 ◽

Vol 115 (2) ◽

pp. 467-474 ◽

Cited By ~ 10

Author(s):

S. Z. Peng ◽

J. Pan

Keyword(s):

Time Domain ◽

Thin Plates ◽

Flexural Waves

Download Full-text

Experiments on cloaking in optics, thermodynamics and mechanics

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2014.0357 ◽

2015 ◽

Vol 373 (2049) ◽

pp. 20140357 ◽

Cited By ~ 8

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.

Download Full-text