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boundary conditions  conditions  elastic  flow  frequency  high frequency  inertia  interface  mechanics  method  model  rate  system  wall inertia  wall 
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Preview: The Quarterly Journal of Mechanics and Applied Mathematics - current issue

The Quarterly Journal of Mechanics and Applied Mathematics Current Issue

Published: Sat, 09 Dec 2017 00:00:00 GMT

Last Build Date: Thu, 01 Feb 2018 05:50:33 GMT


Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening

Sat, 09 Dec 2017 00:00:00 GMT

We consider a dislocation-based rate-independent model of single crystal gradient plasticity with isotropic or linear kinematic hardening. The model is weakly formulated through the so-called primal form of the flow rule as a variational inequality for which a result of existence and uniqueness is obtained using the functional analytical framework developed by Han-Reddy.

The Effect of Wall Inertia on High-Frequency Instabilities of Flow Through an Elastic-Walled Tube

Wed, 15 Nov 2017 00:00:00 GMT

We examine the effect of wall inertia on the onset of high-frequency self-excited oscillations in flow through an elastic-walled tube. The previous asymptotic model of Whittaker et al. (Proc. Roy. Soc. A466, 2010), for a long-wavelength high-frequency instability in a Starling-resistor set-up, neglected inertia in the tube wall. Here, we extend this model by modifying the ‘tube-law’ for the wall mechanics to include inertial effects. The resulting coupled model for the fluid and solid mechanics is solved to find the normal modes of oscillation for the system, together with their frequencies and growth rates. In the system and parameter regime considered, the addition of wall inertia reduces the oscillation frequency of each mode, however its effect on the stability of the system is not as straightforward. Increasing wall inertia lowers the mean flow rate required for the onset of instability, and is therefore destabilising. However, at higher flow rates the instability growth rate is decreased, and so wall inertia is stabilising here. Overall, the addition of wall inertia decreases the sensitivity of the system to the mean axial flow rate. The theoretical results show good qualitative and reasonable quantitative agreement with direct numerical simulations performed using the oomph-lib framework.

Interfacial behaviour in two-fluid Taylor–Couette flow

Tue, 17 Oct 2017 00:00:00 GMT

The flow of a system of two viscous fluids between two concentric counter-rotating cylinders is discussed. A simple theory is presented that describes the evolution of shape of the interface between the fluids when they have near equal densities and identical viscosities. This suggests that the interface is neutrally stable, but that after sufficient time there are nevertheless points on the profile at which the curvature becomes very large. As a consequence, the interface develops cusp-like portions in its profile. A novel spectral method is developed for this problem in which the interface is represented as a region of finite width and over which the density changes rapidly but smoothly. The results confirm the general predictions of the asymptotic theory for rotation in a horizontal plane but when the rotation occurs vertically additional features develop in the flow.

Scaling in Cavity—Expansion Equations using the Isovector Method

Sat, 16 Sep 2017 00:00:00 GMT

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. We use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.

A Direct Method for Bloch Wave Excitation by Scattering at the Edge of a Lattice. Part I: Point Scatterer Problem

Sat, 02 Sep 2017 00:00:00 GMT

A new method for determining the reflection and transmission properties of lattices is developed. The method uses multipole expansions, and certain transformations of the algebraic equation systems that appear when boundary conditions are applied. It is more direct, and much simpler, than earlier approaches based on integral transforms and the Wiener–Hopf technique. The method is demonstrated for the case of a semi-infinite lattice of sound soft acoustic point scatterers, but can easily be generalised to account for finite size effects, and more general boundary conditions.