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

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

Acoustic measurement of lubricant-film thickness distribution in ball bearings

An oil-film thickness monitoring system capable of providing an early warning of lubrication failure in rolling element bearings has been developed. The system is used to measure the lubricant-film thickness in a conventional deep groove ball bearing (shaft diameter 80 mm, ball diameter 12.7 mm). The measurement system comprises a 50 MHz broadband ultrasonic focused transducer mounted on the static outer raceway of the bearing. Typically the lubricant-films in rolling element bearings are between 0.1-1.0 μm in thickness and so are significantly smaller than the ultrasonic wavelength. A quasistatic spring model is used to calculate oil-film thickness from the measured reflection coefficient data. An accurate triggering system has been developed to enable multiple reflection coefficient measurements to be made as the contact ellipse sweeps over the measurement location. Experiments are described in which the loading conditions and rotational speed are varied. Lubricant-film thickness distributions measured ultrasonically are described and are shown to agree well with the predictions from classical elastohydrodynamic (EHD) lubrication theory, particularly at high radial loads and low rotary speeds. A range of parameters affecting the performance of the measurement are discussed and the limits of operation of the measurement technique defined. © 2006 Acoustical Society of America