Wave impedance matrices for cylindrically anisotropic radially inhomogeneous elastic solids

Impedance matrices are obtained for radially inhomogeneous structures using the Stroh-like system of six first order differential equations for the time harmonic displacement-traction 6-vector. Particular attention is paid to the newly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriate to cylinders with material at $r=0$, and its limiting value at that point, the solid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$ is a fundamental material property depending only on the elastic moduli and the azimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ is negative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presented for monoclinic and higher material symmetry, and the special cases of $n=0$ and 1 are treated in detail. Two methods are proposed for finding ${\mathbf Z} (r)$, one based on the Frobenius series solution and the other using a differential Riccati equation with ${\mathbf Z}_0$ as initial value. %in a consistent manner as the solution of an algebraic Riccati equation. The radiation impedance matrix is defined and shown to be non-Hermitian. These impedance matrices enable concise and efficient formulations of dispersion equations for wave guides, and solutions of scattering and related wave problems in cylinders.Comment: 39 pages, 2 figure

Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and their influence on interface behavior is investigated : Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and their dependence on the contact dynamics (friction law, sliding and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.Comment: 17 pages, 10 figure

Effective speed of sound in phononic crystals

A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for $c$ has a more closed form than previous formulas. It significantly improves the efficiency and accuracy of evaluating $c$ for high-contrast composites as demonstrated by a 2D example with extreme behavior.Comment: 4 pages, 1 figur

The ATLAS-SPT Radio Survey of Cluster Galaxies

Using a high-performance computing cluster to mosaic 4,787 pointings, we have imaged the 100 sq. deg. South Pole Telescope (SPT) deep-field at 2.1 GHz using the Australian Telescope Compact Array to an rms of 80 $\mu$Jy and a resolution of 8". Our goal is to generate an independent sample of radio-selected galaxy clusters to study how the radio properties compare with cluster properties at other wavelengths, over a wide range of redshifts in order to construct a timeline of their evolution out to $z \sim 1.3$. A preliminary analysis of the source catalogue suggests there is no spatial correlation between the clusters identified in the SPT-SZ catalogue and our wide-angle tail galaxies.Comment: 9 pages, 4 figures. Submitted to Proceedings of Science for "The many facets of extragalactic radio surveys: towards new scientific challenges", Bologna, Italy 20-23 October 2015 (EXTRA-RADSUR2015