Flexural wave band gaps in locally resonant thin plates with periodically attached spring–mass resonators

Xiao, Yong; Wen, Jihong; Wen, Xisen

doi:10.1088/0022-3727/45/19/195401

Cited by 371 publications

(165 citation statements)

References 33 publications

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“…The arrangement is such that there are N resonators per unit cell located at positions R nα = R n + R α , where n runs for all the lattice vectors and α runs for all the resonators within the unit cell. The governing equation of motion for the plate's displacement W 1 is given by 26 (D∇ 4 …”

Section: Band Structurementioning

confidence: 99%

“…This procedure was employed in Ref. 26; however, in the present work, another form of Eq. (9) is required.…”

Section: Band Structurementioning

confidence: 99%

“…[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.…”

Section: Introductionmentioning

confidence: 99%

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

2013

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An elastic analog of graphene is introduced and analyzed. The system consists of a honeycomb arrangement of spring-mass resonators attached to a thin elastic layer, and the propagation properties of flexural waves along it is studied. The band-structure calculation shows the presence of Dirac points near the K point of the Brillouin zone. Analytical expressions are found for both Dirac frequency and velocity as a function of the resonator's parameters. Finally, the bounded modes of infinitely long ribbons of this honeycomb arrangement are analyzed. The presence of edge states, which are studied using multiple scattering theory, is shown. It is concluded that these structures can be used to control the propagation of flexural waves in thin plates.

show abstract

Section: Band Structurementioning

confidence: 99%

“…This procedure was employed in Ref. 26; however, in the present work, another form of Eq. (9) is required.…”

Section: Band Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2013

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“…The mass-spring oscillator has often been used as the simplest model of a mechanical resonator on the surface of an elastic half-space [17][18][19] or a plate [20,21]. We consider the interaction of horizontal mass-spring oscillators of mass M and spring constant K on the surface z=0 of an elastically isotropic solid half-space with a shear horizontal wave propagating in the x direction and polarized in the y direction.…”

Section: Acoustic Case: Interaction Of Sh Wave In a Solid Half-spmentioning

confidence: 99%

Waveguiding by a locally resonant metasurface

Maznev

Gusev

2015

Phys. Rev. B

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Dispersion relations for acoustic and electromagnetic waves guided by resonant inclusions located at the surface of an elastic solid or an interface between two media are analyzed theoretically within the effective medium approximation. Oscillators on the surface of an elastic half-space are shown to give rise to a Love-type surface acoustic wave only existing below the oscillator frequency. A simple dispersion relation governing this system is shown to also hold for electromagnetic waves guided by Lorentz oscillators at an interface between two media with equal dielectric constants. Different kinds of behavior of the dispersion of the resonantly guided mode depending on whether the bulk wave in the absence of oscillators can propagate along the surface or interface are identified.

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“…The local resonances have been achieved by introducing surface "inclusions" on top of semi-infinite mediums 16 or thin plates, such as hollow spheres or cylinders, 17 springmasses, 18,19 simple pillars, 20 or composite pillars. 21 Experiments have been reported proving the existence of tunable band gaps by using stubs 22,23 or piezoelectric shunts 24 on plates.…”

Section: Introductionmentioning

confidence: 99%

Scattering of flexural waves from a hole in a thin plate with an internal beam

Climente

Norris

Sánchez‐Dehesa

2015

The Journal of the Acoustical Society of America

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The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.

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Flexural wave band gaps in locally resonant thin plates with periodically attached spring–mass resonators

Cited by 371 publications

References 33 publications

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

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

Waveguiding by a locally resonant metasurface

Scattering of flexural waves from a hole in a thin plate with an internal beam

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