Scattering of flexural waves from an N-beam resonator in a thin plate

Abstract

The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an N -beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the background plate by a number N of rectangular beams. After representing the boundary conditions in a modal multipole expansion form, a compact expression is obtained for the T-matrix, which relates the incident and the scattered transverse (out-of-plane) waves. The analysis of the scattering cross-section reveals interesting scattering features, like resonances and anisotropy, associated to this type of resonators. Numerical experiments performed within the framework of the finite element method support the accuracy of the model here developed. * Corresponding author: jsdehesa@upv.es 2

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

“…The barrier consists of three layers of two-beam resonators. 9 There are two main reasons justifying the choice of this type of resonators. First, the resonance induced bandgap can be easily tuned to specific working frequencies by changing the geometric parameters.…”

“…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

“…In a previous work [44], the multiple scattering approach was applied to develop a semi-analytical model allowing the calculation of the band structure of flexural waves propagating in a thin plate containing a lattice of resonant cavities. The cavities consist of N -beam resonators, whose corresponding Tmatrix was derived by applying the impedance matrix method [46]. In this section, we develop a similar procedure but now applied to the case of cavities containing a certain number M of 1-beam resonators.…”

“…In polar coordinates, the out-of-plane displacements in the background plate, W (R, Θ), and in the nth circular plate, W n (r, θ), can be expressed as [44,46]…”

“…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.…”