ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Recently Published Articles
- Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators
Hamid M. Sedighi, Farhang Daneshmand and Mohamadreza Abadyan
Article first published online: 20 JUL 2015 | DOI: 10.1002/zamm.201400160
Dynamic pull-in behavior of nonlocal functionally graded nano-actuators by considering Casimir attraction is investigated in this paper. It is assumed that the nano-bridge is initially at rest and the fundamental frequency of nano-structure as a function of system parameters is obtained asymptotically by Iteration Perturbation Method (IPM). The effects of actuation voltage, nonlocal parameter, properties of FGM materials and intermolecular force on the dynamic pull-in behavior are studied. It is exhibited that two terms in series expansions are adequate to achieve the acceptable approximations for fundamental frequency as well as the analytic solution. Comparison between the obtained results based on the asymptotic analysis and the reported experimental and numerical results in the literature, verify the effectiveness of the asymptotic analysis.
- A generalization of Noether's theorem for a non-material volume
Leonardo Casetta, Hans Irschik and Celso Pupo Pesce
Article first published online: 20 JUL 2015 | DOI: 10.1002/zamm.201400196
Variable-mass conditions can occur in a variety of practical problems of engineering. Investigations on problems of this type have been figuring as a particular research field of mechanics and applied mathematics. The fundamental issue is that the basic equations of classical mechanics were originally formulated for the case of an invariant mass contained in a material volume. Therefore, appropriate formulations are required when dealing with variable-mass problems. The scope of the present article is devoted to arbitrarily moving control volumes formulated within the framework of Ritz's method, that is, to non-material volumes in the sense discussed by Irschik and Holl . We aim at demonstrating a generalized version of Noether's theorem such that it can be grounded on the generalized Hamilton's principle for a non-material volume in the form derived by Casetta and Pesce . This will consistently allow the consideration of conservation laws, written from a Noetherian approach, in this particular context of non-material volumes. To test the proposed formulation, the problem of a rotating drum uncoiling a strip will be addressed.
- The Riemann problem for the Chaplygin gas equations with a source term
Article first published online: 20 JUL 2015 | DOI: 10.1002/zamm.201500015
The Riemann solutions for the one-dimensional Chaplygin gas equations with a Coulomb-like friction term are constructed explicitly. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine-Hugoniot conditions of delta shock wave are established and the position, propagation speed and strength of delta shock wave are given, which enables us to see the influence of Coulomb-like friction term on the Riemann solutions for the Chaplygin gas equations clearly. In addition, the relations connected with the area transportation are derived which include mass and momentum transportation.
- The motion induced by a radially stretching membrane in a rotating fluid system
Patrick D. Weidman
Article first published online: 16 JUL 2015 | DOI: 10.1002/zamm.201500094
The flow induced above an impermeable sheet undergoing linear radial stretching in a system rotating at angular velocity Ω is investigated. The problem is governed by the single parameter , where a is the stretching rate of the membrane. A similarity reduction of the Navier-Stokes equations leads to a pair of nonlinearly-coupled ordinary differential equations which are numerically solved over the range . Coriolis forces acting on the radially stretching flow in the vicinity of the wall induces azimuthal flow in the boundary layer. A large-σ analysis of the system leads to the Ekman equations describing the balance of Coriolis and viscous forces for which an exact solution is presented. Numerical results for the radial and azimuthal shear stresses, along with the magnitude of the velocity induced into the boundary layer, are shown to be in good agreement with the large-σ asymptotic results.
- Generation of shocks by the Biermann battery
Article first published online: 16 JUL 2015 | DOI: 10.1002/zamm.201500034
The generation of magnetic field in shock surfaces separating regions of different electron density is a well known phenomenon. We study how this generation will affect the original structure of ionic flow. In a one-dimensional geometry, it turns out that the leading magnetosonic wavefront produced by the seed field may be compressional, ultimately evolving into a shock in a finite time. The time where this shock occurs depends on few parameters: sound velocity, Alfvén velocity and the variation of the magnetic field at the original surface at time zero. The alternative is that the magnetosonic wave may stabilize or damp out, which always happens if we start from a null magnetic field.