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

Cover image for Vol. 93 Issue 12

December 2013

Volume 93, Issue 12

Pages 841–976

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Cover Picture: ZAMM 12 / 2013

      Article first published online: 2 DEC 2013 | DOI: 10.1002/zamm.201390020

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Issue Information: ZAMM 12 / 2013

      Article first published online: 2 DEC 2013 | DOI: 10.1002/zamm.201390021

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Contents: ZAMM 12 / 2013 (pages 841–843)

      Article first published online: 2 DEC 2013 | DOI: 10.1002/zamm.201309312

  4. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Some theoretical and computational aspects of single-crystal strain-gradient plasticity (pages 844–867)

      B.D. Reddy

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201200101

      Thumbnail image of graphical abstract

      Variational formulations are constructed for rate-independent problems in single-crystal strain-gradient plasticity. The framework makes use of the flow rule expressed in terms of a dissipation function. The formulation extends to the finite deformation context earlier work on this problem. Provision is made for energetic and dissipative microstresses, and a range of defect energies is accounted for. The minimization problem corresponding to the time-discrete formulation is derived.

  5. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. A discrete-mechanical approach for computation of three-dimensional flows (pages 868–881)

      B.E. Abali, W.H. Müller and D.V. Georgievskii

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201300080

      Thumbnail image of graphical abstract

      Dynamical processes modeled with a suitable set of differential equations can be approximately computed with finite element method. However, especially in fluid dynamics, numerical instabilities may occur. In order to circumvent such problems many techniques have been realized over the last four decades. Often the lack of stability is linked to numerical insufficiency, therefore the solution is sought by tuning functional spaces. Stabilizing terms are needed and helpful, however, they involve coefficients to be found depending on the underlying problem. The purpose of this work is to propose another approach based on first principles producing similar terms so that the numerical approximation converges without using any other parameter but the material constants, which are measurable.

    2. Global well-posedness of the aggregation equation with supercritical dissipation in Besov spaces (pages 882–894)

      G. Wu and Q. Zhang

      Article first published online: 30 JAN 2013 | DOI: 10.1002/zamm.201200167

      The authors study the supercritical aggregation equation. They prove the global well-posedness for small initial data lying in Besov spaces and the local well-posedness for arbitrary initial data. The Fourier localization technique and the Littlewood-Paley theory are the main tools used in the proof.

    3. The undulatory motion of a chain of particles in a resistive medium in the case of a smooth excitation mode (pages 895–913)

      N. Bolotnik, M. Pivovarov, I. Zeidis and K. Zimmermann

      Article first published online: 30 JAN 2013 | DOI: 10.1002/zamm.201200124

      Thumbnail image of graphical abstract

      The motion of a chain of three identical bodies along a straight line in a dry-friction medium is studied. The motion is excited and controlled by changing the distances between the bodies of the chain. An undulatory excitation mode is proposed, in which the distances between the adjacent bodies of the chain change periodically and the time histories of the distances in the pairs of adjacent bodies consecutively repeat each other with a constant time shift. It looks like a wave is running along the chain. The necessary and sufficient conditions for the system to be able to move from rest are established.

    4. Propagation of linear compression waves through plane interfacial layers and mass adsorption in second gradient fluids (pages 914–927)

      G. Rosi, I. Giorgio and V.A. Eremeyev

      Article first published online: 1 MAR 2013 | DOI: 10.1002/zamm.201200285

      Thumbnail image of graphical abstract

      This paper addresses the problem of reflection and transmission of compression waves at the phase transition layer between the vapour and liquid phases of the same fluid. Within the framework of second gradient fluid modeling, the authors use a nonconvex free energy in order to describe the phase transition phenomenon. A stationary solution for the fluid density is found for an infinite domain, and an analytical expression for the phase transition is presented. Then the propagation of linear waves superposed to this stationary solution is discussed.

    5. On the instability of equilibrium position of a mechanical system with singular constraints (pages 928–936)

      V. Čović, Z. Mitrović, S. Rusov and A. Obradović

      Article first published online: 18 FEB 2013 | DOI: 10.1002/zamm.201200080

      The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems.

    6. Propagation of dilatation and shear waves through a dynamic checkerboard material geometry in 1D space + time (pages 937–943)

      W.C. Sanguinet and K.A. Lurie

      Article first published online: 26 AUG 2013 | DOI: 10.1002/zamm.201200249

      Thumbnail image of graphical abstract

      Two isotropic materials alternate occupying rectangular cells in 1D space + time producing a double periodic checkerboard material assembly. The materials are assumed to differ in their wave velocities (dilatational and shear) and to have pairwise equal values of wave impedances for each type of wave. The authors show, however, that, for both types of waves traveling normally to spatial interfaces between the materials, the average velocity of propagation is the same for certain ranges of material and structural parameters.

    7. A perturbative model for predicting the high-Reynolds-number behaviour of the streamwise travelling waves technique in turbulent drag reduction (pages 944–962)

      M. Belan and M. Quadrio

      Article first published online: 22 FEB 2013 | DOI: 10.1002/zamm.201200153

      Thumbnail image of graphical abstract

      The background of this work is the problem of reducing the aerodynamic turbulent friction drag, which is an important source of energy waste in innumerable technological fields. The authors focus on one recently proposed and very promising technique.

    8. Scattering of plane acoustic waves by a circular semi-infinite pipe with a rigid end face placed axially in an infinite circular duct (pages 963–976)

      Ö. Yanaz Çınar

      Article first published online: 21 JAN 2013 | DOI: 10.1002/zamm.201200062

      Thumbnail image of graphical abstract

      In this paper, the propagation of acoustic waves along a duct system, where a semi-infinite circular rigid pipe with a rigid end face is placed axially inside an infinite circular rigid pipe is analyzed rigorously. First, direct Fourier transform is applied and the problem is reduced into the solution of a modified Wiener-Hopf equation of the second type from which the reflection and transmission coefficients are determined. Then the bifurcated circular waveguide problem is solved by applying direct Fourier transform again to reduce the problem into the solution of a Wiener-Hopf equation and the resulting transfer coefficients are taken into account when applying the building block method.

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