Focussing bending waves via negative refraction in perforated thin plates

Abstract

International audienceWe propose a design of a periodically perforated thin plate leading to lensing effect of bending waves via negative refraction. To achieve this goal, we first analyze the band spectrum of the bi-harmonic operator for an array of freely vibrating square voids using both numerical finite elements and asymptotic methods. We then find some point in the reciprocal space where the acoustic dispersion surface displays a convex isofrequency contour shrinking with frequency. We finally demonstrate that a point force generating a bending wave above a finite array of 221 perforations displays an image underneath according to the Snell–Descartes inverted laws

Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

“…[19][20][21][22] An elastic analog of graphene has not been fully analyzed, although the effort to create structures to control the propagation of elastic waves in 2D systems has been remarkable. Thus phononic band-gap systems for Lamb waves have been widely studied, [23][24][25][26][27] as well as advanced refractive structures [28][29][30] or more complex devices based on the transformation-coordinate method. [31][32][33] This work presents an elastic analog of graphene.…”

Negative refraction of elastic waves in 2D phononic crystals: Contribution of resonant transmissions to the construction of the image of a point source

“…Nevertheless, negative refraction of shear waves or of transverse waves was analyzed numerically in periodic arrays of holes drilled in a metal matrix. 9,10 More recently such phenomenon was reported for surface modes 11 or for plate modes 12,13 It is straightforward that superlenses based on solid matrix phononic crystals may have potential applications in the fields of medical imaging or ultrasonic beam-based therapy provided the negative refraction and then the focusing phenomenon involve longitudinal waves. Indeed it is necessary for this kind of applications, that the phononic crystal lens be surrounded by a fluid medium.…”

Beam paths of flexural Lamb waves at high frequency in the first band within phononic crystal-based acoustic lenses

“…9,10 These studies of acoustic waves in fluids have inspired a series of works dealing with other polarized waves both on the negative refraction phenomenon [11][12][13] and on the focusing of negative-refractive PCs. [14][15][16][17][18] On the other hand, there has been a great deal of work on systems based onto a positive refraction process to realize the focusing. In the relatively early studies, [19][20][21][22] the PCs were usually composed of an uniform structure with various geometrical shapes, and the same physical limitations as for conventional optical lenses were therefore observed.…”