Theoretical study of platonic crystals with periodically structured N-beam resonators

Abstract

A multiple scattering theory is applied to study the properties of flexural waves propagating in a plate with periodically structured N -beam resonators. Each resonator consists of a circular hole containing an inner disk connected to background plate with N rectangular beams. The Bloch theorem is employed to obtain the band structure of a two-dimensional lattice containing a single resonator per unit cell. Also, a numerical algorithm has been developed to get the transmittance through resonators slabs infinitely long in the direction perpendicular to the incident wave. For the numerical

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

“…Second, two beams contribute to bandgap enhancement when they are arranged in parallel with the wavefront of the incident waves. 10,16 The geometric parameters described in Fig. 6(a) are R 1 ¼ 4 mm, R 2 ¼ 7 mm, b ¼ 2 mm, and l ¼ 20 mm.…”

“…On the one hand, the transmission properties of flexural waves through lattices of typical scatterers, like inclusions and free or clamped holes, have been obtained in the framework of the multiple scattering formalism. 10,11 The accuracy of the semianalytical method has been fully demonstrated in the original works, therefore the relevant results will be directly used in this work without any repetition of details. On the other hand, due to the difficulties in solving transcendental equations with complex solutions, 6 a commercial finite element package (COMSOL Multiphysics) is employed to conduct the eigenfrequency analysis in three-dimensional (3-D) solid mechanics module where full elastic equations are taken into consideration.…”

“…Particularly, our interest concentrates on the first order asymmetric Lamb mode, also termed as a flexural wave, whose behavior is well described by a biharmonic equation based on Kirchhoff-Love plate theory. [8][9][10] By considering arrays of free holes we can adjust the scattering strength by merely changing the radius of the holes. It is shown later that the lowest order symmetric leaky guided mode (S0 mode) evolves with increasing radius, offering a new freedom to manipulate the propagation of flexural waves.…”

Single-phase metamaterial plates for broadband vibration suppression at low frequencies

“…The aspect has attracted considerable interest in the community in recent years [6,12,14,[37][38][39][40][41][42][43][44][45]. The previous works reported interesting applications in superlensing [39,40], focusing [6,44], directional wave guiding [12] and vibration shielding [37,38,41,42,45]. Among these works, most of them were performed within the framework of the finite element method because of the structural complexity.…”

“…However, if the resonant microstructure is specially designed with simple geometries like rectangular beams and circular plates, such as the N -beam resonators proposed in Ref. [46], the theoretical study of the corresponding platonic crystals can be easily performed by combining the impedance matrix method with the multiple scattering method [44]. In most cases, the numerical computing based on the self-developed modeling is much more efficient than the finite-elementbased software when dealing with multiple scattering systems because the latter requires a huge number of elements to ensure accuracy.…”