# ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Editor: Holm Altenbach

Impact Factor: 1.008

ISI Journal Citation Reports © Ranking: 2013: 76/251 (Mathematics Applied); 79/139 (Mechanics)

Online ISSN: 1521-4001

Associated Title(s): GAMM-Mitteilungen, Mathematische Nachrichten, Mathematical Logic Quarterly, PAMM

### Recently Published Issues

Current Issue:April 2015

Volume 95, Issue 4

Volume 95, Issue 3

Volume 95, Issue 2

Volume 95, Issue 1

Volume 94, Issue 12

### Recently Published Articles

- When is natural convection completely passive?
Anthony Kay

Article first published online: 16 APR 2015 | DOI: 10.1002/zamm.201400177

Momentum and energy equations for vertical flow with viscous dissipation are derived and shown to require that the cross-section mean density is taken as the reference density for calculation of buoyancy forces under the Boussinesq approximation. Solutions are obtained for flow between parallel plane walls, with and without the pressure work as an explicit term in the energy equation. Both walls are at the same temperature, so there is no thermal forcing, but solutions are obtained for all admissible values of dynamic pressure gradient. The passive convection condition, whereby the flow is driven entirely by buoyancy forces resulting from heat generated by the flow's own viscous dissipation, is found on one branch of the dual solutions. However, while theoretically possible, passive convection is not physically realisable with any real fluid.

- Elastodynamics of strongly heterogeneous periodic plates using Reissner-Mindlin and Kirchhoff-Love models
Eduard Rohan and Bernadette Miara

Article first published online: 16 APR 2015 | DOI: 10.1002/zamm.201400145

The paper deals with the homogenization of strongly heterogeneous elastic plates satisfying the Reissner-Mindlin or the Kirchhoff-Love hypotheses. We rigorously justify the limit models obtained by the asymptotic analysis which describe the harmonic waves propagation associated with in-plane displacement and transversal deflection modes in these two classical plate structures. Large contrasts in the coefficients of the elastic material components may result in existence of band gaps for the limit Reissner-Mindlin plates while an analogous property is lost for the deflection of the Kirchhoff-Love model. The different dispersion properties of both the limit plates are related to the changing sign of the limit frequency dependent mass density coefficients.

- The motion of a two-body limbless locomotor along a straight line in a resistive medium
N. Bolotnik, M. Pivovarov, I. Zeidis and K. Zimmermann

Article first published online: 14 APR 2015 | DOI: 10.1002/zamm.201400302

The behavior of a two-body self-propelling locomotion system in a resistive environment is studied. The motion of the system is excited and sustained by means of a periodic change in the distance between the bodies. A complete analysis of the motion of the system is performed for the case where the resistance forces applied by the environment to the bodies of the system are represented by linear functions of the velocities of these bodies relative to the environment. For the case where the resistance forces are nonlinear functions of the velocities of the bodies, a model based on the averaged equation of motion is used. This model assumes the forces of friction acting in the system to be small in comparison with the excitation force. The motion of the system along a horizontal straight line in an isotropic dry friction environment is investigated in detail for two particular types of excitation modes. The calculated results are compared with the experimental data.

- A penny-shaped magnetically dielectric crack in a magnetoelectroelastic cylinder under magnetoelectromechanical loads
L. L. Liu, W. J. Feng and P. Ma

Article first published online: 13 APR 2015 | DOI: 10.1002/zamm.201500049

In this paper the fracture behaviors of magnetoelectroelastic cylinder induced by a penny-shaped magnetically dielectric crack are investigated. By employing the Hankel transform technique and introducing three auxiliary functions, the complex question is transformed to solve three coupled nonlinear Fredholm integral equations. The intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are derived in closed forms. The effects of the radius of the cylinder, applied electric field and magnetic field, dielectric permittivity and magnetic permeability of the crack interior on the COD intensity factor are illustrated numerically. The results corresponding to magnetoelectrically permeable and impermeable boundary conditions are only the special cases of the present model.

- On PDE analysis of flows of quasi-incompressible fluids
Eduard Feireisl, Yong Lu and Josef Málek

Article first published online: 11 APR 2015 | DOI: 10.1002/zamm.201400229

We study mathematical properties of quasi-incompressible fluids. These are mixtures in which the density depends on the concentration of one of their components. Assuming that the mixture meets mass and volume additivity constraints, this density-concentration relationship is given explicitly. We show that such a constrained mixture can be written in the form similar to compressible Navier-Stokes equations with a singular relation between the pressure and the density. This feature automatically leads to the density bounded from below and above. After addressing the choice of thermodynamically compatible boundary conditions, we establish the large data existence of weak solution to the relevant initial and boundary value problem. We then investigate one possible limit from the quasi-compressible regime to the incompressible regime.