Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate

Abstract

We investigate theoretically the band structure of a phononic crystal of finite thickness constituted of a periodical array of cylindrical dots deposited on a thin plate of a homogeneous material. We show that this structure can display a low-frequency gap, as compared to the acoustic wavelengths in the constituent materials, similarly to the case of locally resonant structures. The opening of this gap requires an appropriate choice of the geometrical parameters, and in particular the thickness of the homogeneous plate and the height of the dots. However, the gap persists for various combinations of the materials constituting the plate and the dots. Besides, the band structure can exhibit one or more higher gaps whose number increases with the height of the cylinders. We discuss the condition to realize waveguiding through a linear defect inside the phononic crystal dots. The numerical simulations are performed by using the finite difference time domain and the finite element methods.

Waveguiding by a locally resonant metasurface

“…A mention should be made of studies of acoustic modes of stubbed plates [35][36][37]. The situation here is more akin to that shown in Fig.…”

Phonon and heat transport control using pillar-based phononic crystals

“…The frequency of the Bragg bandgap is linked to the period of the PnCs and thus affects only phonons with the wavelengths of about the characteristic size of the system [27,35,37]. The frequencies of the local resonance bandgaps are linked to the resonant frequencies of the pillars [27], which can be tuned via structural parameters, such as pillar diameter [30,38] and height [25,26,30,38,39], or material parameters, such as density and Young modulus [25,30]. Thus, the local resonance bandgaps can be opened at higher [27] or lower [39,40] frequencies than the Bragg bandgap.…”

“…A decade ago, Pennec et al [25] and Wu et al [26] proposed that the mechanical properties of a thin plate can be changed by depositing external periodic pillars on the surface of the plate, thus forming the pillar-based PnC. Since then, many theoretical and experimental works studied pillar-based PnCs and their applications in mechanical and thermal engineering.…”

Pillar-type acoustic metasurface

“…This has been demonstrated both numerically and experimentally, with 1D stripes periodically engraved on the surface of a lithium niobate substrate 8 and more recently with 2D phononic crystals made of a periodical array of cylindrical pillars deposited on a thin and homogeneous slab. [9][10][11][12][13][14][15][16][17][18] This last structure deserves special attention. Indeed, a pillar exhibits both compressional (monopolar) and bending (dipolar) resonances that may lead to negative dynamic effective modulus and mass density respectively.…”