Phononic layered composites for stress-wave attenuation

Abstract

The aim is to design a layered metamaterial with high attenuation coefficient and high in-plane stiffnessto-density ratio using homogenization to calculate and optimize the dynamic effective stiffness and mass density of layered periodic composites (phononic layers) over a broad frequency band. This is achieved by: (1) minimizing the frequency range of the first pass band, (2) maximizing the frequency range of the stop band, and (3) creating local resonance over the second pass band. To verify the theoretical calculation, laboratory samples were fabricated and their attenuation coefficient were measured and compared with the theoretical results. It is observed that over 4 to 20 kHz frequency range the attenuation per unit length in the optimally designed composite can exceed 500 dB/m; which increases with increasing frequency. A dynamic Ashby chart, depicting attenuation coefficient vs. in-plane stiffness-todensity ratio, is presented for various engineering materials and is compared with the fabricated metamaterial to show the significance of our design. This method can be used in variety of applications for stress wave management, e.g., in addition to match the impedance of the resulting composite to that of its surrounding medium to minimize (or essentially eliminate) stress wave reflection.

Waves in one-dimensional quasicrystalline structures: dynamical trace mapping, scaling and self-similarity of the spectrum

“…(13), we can easily deduce that all the information concerning wave propagation in a structure whose elementary cell is generated according to the arbitrary sequence F i is contained in the trace trT i of the corresponding transfer matrix. The transfer matrix method has been extensively used to study the dynamics of periodic laminates (Willis, 2016), multilayered materials with structured interfaces (Brun et al, 2010) and phononic crystals (Wu et al, 2009;Nemat-Nasser et al, 2015). It has been extended to multi-phase flexural systems by Romeo and Luongo (2002); Carta and Brun (2015); Shmuel and Pernas-Salomon (2016).…”

Two-Dimensional Phononic Crystals With Acoustic-Band Negative Refraction

“…Consider a two-dimensional PC with rectangular inclusions and a unit cell shown in Figure 1. For a unit cell of the PC with the edges defined by 1, 2 , the periodicity condition can be expressed as (1) where is the position vector, is the density, is the elasticity tensor, and can be any integer.…”

Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array

“…Various methods have been developed for band structure calculation. Transfer Matrix (TM) method is widely used 5,[13][14][15][16][17][18] in 1D periodic beams and multi-layered structure. However, the TM method usually can only be applied in one direction.…”