Harmonic waves in a solid with a periodic distribution of spherical cavities

Abstract

A dispersion relation has been obtained for the propagation of harmonic waves in an elastic solid containing a three-dimensional array of regularly spaced spherical cavities of equal radius. The general pattern of the frequency spectrum is one of passing and stopping bands. Results are presented for the lowest acoustic mode, the transition to the first optical mode, and for a segment of the first optical mode.

Transfer matrix approach of vibration isolation analysis of periodic composite structure

“…To write down a general form of this series representation, it is convenient to employ the usual displacement decomposition of u S r (x) in terms of a scalar potential φ(x) and a vector potential ψ(x) [4] …”

“…Esquivel-Sirvent and Cocoletzi [3] deduced reflectivity and dispersion relation of elastic wave propagating in periodic layered composite structures. Achenbach et al analyzed the band gap of an elastic wave in periodic medium with all kinds of cave [4][5][6][7][8].…”

Complete band gaps in two-dimensional piezoelectric phononic crystals with {1–3} connectivity family

“…Various structures and compositions of composite materials have been investigated using different approaches (Bai and Keller, 1987;Achenbach and Kitahara, 1987;Hennion et al, 1990;Hladky-Hennion and Decarpigny, 1991). Moreover, during the last few years, much effort has focused on the search of large band gaps in the acoustic band structures of periodic inhomogeneous composite systems.…”

Acoustic Bloch Wave Propagation in a Periodic Waveguide

“…In order for these two constraints to be consistent with one another, a particular dispersion relation must exist. In the analysis presented here, which parallels that of Achenbach and Kitahara (1987), the Bloch condition is imposed in the form of boundary conditions. These boundary conditions, which are derived from the Bloch conditions, are applied at the centers of neighboring cells, as shown in Fig.…”

“…While the side branches do not generally represent small perturbations in the cross sectional area of a waveguide, they do represent spatially localized perturbations. An approach which is readily applicable when the nonuniformity in the waveguide is spatially localized (and more generally applicable) is that of Achenbach and Kitahara (1987). They treat the problem of wave propagation in an elastic solid that has a three dimensional rectangular lattice of spherical cavities.…”