Metamaterials: supra\textit{supra}-classical dynamic homogenization

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material parameters that can be electronic, magnetic, acoustic, or elastic, and must adequately represent the wave interaction behaviour in the composite within desired frequency ranges. In some cases -- for example, the low frequency regime -- there exist various efficient ways by which effective material parameters for wave propagation in metamaterials may be found. However, the general problem of predicting frequency-dependent dynamic effective constants has remained unsolved. Here, we obtain novel mathematical expressions for the effective parameters of two-dimensional metamaterial systems valid at higher frequencies and wavelengths than previously possible. By way of an example, random configurations of cylindrical scatterers are considered, in various physical contexts: sound waves in a compressible fluid, anti-plane elastic waves, and electromagnetic waves. Our results point towards a paradigm shift in our understanding of these effective properties, and metamaterial designs with functionalities beyond the low-frequency regime are now open for innovation.Comment: 14 pages (including 4 figures and 1 table) in New Journal of Physics, 201

Operating limits for acoustic measurement of rolling bearing oil film thickness

An ultrasonic pulse striking a thin layer of liquid trapped between solid bodies will be partially reflected. The proportion reflected is a function of the layer stiffness, which in turn depends on the film thickness and its bulk modulus. In this work, measurements of reflection have been used to determine the thickness of oil films in elastohydrodynamic lubricated (EHL) contacts. A very thin liquid layer behaves like a spring when struck by an ultrasonic pulse. A simple quasi-static spring model can be used to determine the proportion of the ultrasonic waves reflected. Experiments have been performed on a model EHL contact between a ball and a flat surface. A transducer is mounted above the contact such that the ultrasonic wave is focused onto the oil film. The reflected signals are captured and passed to a PC for processing. Fourier analysis gives the reflection spectrum that is then used to determine the stiffness of the liquid layer and hence its thickness. In further testing, an ultrasonic transducer has been mounted in the housing of a deep-groove ball bearing to measure the film generated at the outer raceway as each ball passes. Results from both the ball-flat and ball bearing measurements agree well with steady-state theoretical EHL predictions. The limits of the measuring technique, in terms of the measurable rolling bearing size and operating parameters, have been investigated

Three-dimensional ultrasonic colloidal crystals

Colloidal assembly represents a powerful method for the fabrication of functional materials. In this article, we describe how acoustic radiation forces can guide the assembly of colloidal particles into structures that serve as microscopic elements in novel acoustic metadevices or act as phononic crystals. Using a simple three-dimensional orthogonal system, we show that a diversity of colloidal structures with orthorhombic symmetry can be assembled with megahertz-frequency (MHz) standing pressure waves. These structures allow rapid tuning of acoustic properties and provide a new platform for dynamic metamaterial applications.Comment: 23 pages (including 12 figures

On the radiation force fields of fractional-order acoustic vortices

Here we report the creation and observation of acoustic vortices of fractional order. Whilst integer orders are known to produce axisymmetric acoustic fields, fractional orders are shown to break this symmetry and produce a vast array of unexplored field patterns, typically exhibiting multiple closely spaced phase singularities. Here, fractional acoustic vortices are created by emitting ultrasonic waves from an annular array of sources using multiple ramps of phase delay around its circumference. Acoustic radiation force patterns, including multiple concentration points, short straight lines, triangles, squares and discontinuous circles are simulated and experimentally observed. The fractional acoustic vortex leading to two closely spaced phase singularities is used to trap, and by controlling the order, reversibly manipulate two microparticles to a proximity of 0.3 acoustic wavelengths