Geometry of Miura-folded metamaterials.

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Investigation of the effect of combustor cooling geometry on acoustic energy absorption

To control combustion instabilities occurring in LPP gas turbine combustors, several active and passive systems have been developed in recent years. The combustion chamber cooling geometry has the potential to influence instability feedback loops by absorbing acoustical energy inside the combustor. The design of the cooling liner and the geometry of the cooling plenum and the cooling air flow rate have a significant influence on the absorption characteristics of the system. This paper presents the results of a cold flow study which was carried out in the course of a comprehensive study on the influence of the cooling geometry on combustor thermoacoustics. Absorption characteristics of three different cooling liner geometries and non-perforated plates were determined over a frequency range from 50 Hz to 600 Hz for different cooling flow rates and different cooling plenum volumes. The experimental results compared well with results from a low order thermoacoustic network model. The acoustic energy absorption spectrum of a cooling liner with 90°-hole configuration was found to be strongly dependent on cooling flow rate and cooling plenum volume, whereas the absorption spectrum of cooling liners with 25°-holes were found to be strongly dependent on the cooling plenum volume, but less dependent on the cooling air flow rate. All cooling liner setups with perforations were capable of increased acoustic absorption over a broad band of frequencies compared to the case of non-perforated combustor walls. © 2010 by Johannes Schmidt.

Optimization of nanotube electrode geometry in a liquid crystal media from wavefront aberrations

This paper presents experimental optimization of number and geometry of nanotube electrodes in a liquid crystal media from wavefront aberrations for realizing nanophotonic devices. The refractive-index gradient profiles from different nanotube geometries-arrays of one, three, four, and five-were studied along with wavefront aberrations using Zernike polynomials. The optimizations help the device to make application in the areas of voltage reconfigurable microlens arrays, high-resolution displays, wavefront sensors, holograms, and phase modulators. © 2012 Optical Society of America.

Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

Geometry and interaction of structures in homogeneous isotropic turbulence

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number Reλ = 141 is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, L. The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, planarity' and filamentarity', obtained using the Minkowski functionals. The planarity increases gradually by a small amount as L is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as L decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale L are most likely to align with the largest extensional strain at a scale 3-5 times larger than L. This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the 5η scale (where η is the Kolmogorov scale) are more concentrated near the ones that are 3-5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures. Copyright © 2012 Cambridge University Press.

Sources of variability in the free-ball micro-scale abrasion test

In the 'free-ball' version of the micro-scale abrasion or ball-cratering test the rotating ball rests against a tilted sample and a grooved drive shaft. Tests under nominally identical conditions with different apparatus commonly show small but significant differences in measured wear rate. An indirect method has been developed and demonstrated for continuous on-line measurement of the coefficient of friction in the free-ball test. Experimental investigation of the effects of sample tilt angle and drive shaft groove width shows that both these factors influence the stability of the rotation of the ball, and the shape of the abrasive slurry pool, which in turn affect the coefficient of friction in the wear scar area and the measured wear rate. It is suggested that in order to improve the reproducibility of this method the geometry of the apparatus should be specified. For the apparatus used in this work with a steel ball of 25 mm diameter, a sample tilt angle of 60-75° and a shaft groove width of about 10mm provided the most stable ball motion and a wear rate which showed least variability. © 2004 Elsevier B.V. All rights reserved.