《Wave Motion》2015

The transmission and reflection of one-component elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of one-component waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of one-component waves.  相似文献   

    

《Wave Motion》2015

In this paper, a double orthogonal polynomial series method is proposed to investigate the guided wave propagation in a two-dimensional (2-D) structure, namely, a FGM ring with a rectangular cross-section. Two kinds of graded rings are considered: material gradient directions being in the radial direction and in the axial direction respectively. Numerical comparison with available reference results for a straightly homogeneous rectangular bar illustrates the validity of the proposed method. The dispersion curves and displacement distributions of various FGM rings, which have different radius to thickness ratios, different material gradient directions and different thickness to height ratios, are calculated to reveal the guided wave characteristics.  相似文献   

    

《Wave Motion》2015

We re-examine a simple model describing the propagation of transient forced internal gravity waves in a Boussinesq fluid with constant horizontal mean velocity which was previously studied by Nadon and Campbell (Wave Motion, 2007). The waves are generated by a horizontally-periodic lower boundary condition and propagate upwards. We derive an alternative exact expression for the solution which more readily gives insight into the behaviour of the solution at high altitude. Some special cases of lower boundary conditions are considered to illustrate the features of the solution. This form of the solution allows us to use a Fourier transform to derive the solution for the more general situation where a wave packet is generated by a horizontally-localized lower boundary condition, comprising a continuous spectrum of horizontal wavenumbers or Fourier modes. This is a more realistic representation of internal gravity waves in the atmosphere and can be used as a starting point for investigating waves generated by an obstacle of finite horizontal extent such as an isolated mountain or a mountain range.  相似文献   

    

H.C. Kuhlmann  S. Albensoeder 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2005,85(6):387-399

Vortices are of fundamental importance in fluid mechanics. An interesting aspect of vortex dynamics is the transition from two‐ to three‐dimensional flow. The transition to three‐dimensional flow of a circular vortex can be caused by a weak two‐dimensional non‐axisymmetric strain field deforming the circular streamlines. After briefly reviewing the three‐dimensional instability of strained vortices in unbounded domains, the effect on vortex stability of bounding walls of an enclosure will be investigated by exploring the 2D–3D transition in a driven cavity. This system, in which the flow is driven by the steady tangential motion of one or two facing walls, is a paradigm for closed flows. The rich multitude of instabilities and bifurcations is demonstrated and analogies to unstable unbounded vortices are established. Contrary to vortices in open flows, the amplitudes of three‐dimensional perturbations in driven cavities typically saturate. Hence, stationary or time‐periodic three‐dimensional vortices can be realized with ease, facilitating detailed experimental investigations.  相似文献   

    

M. Stoffel 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2005,85(9):643-659

In the present paper measured and simulated vibrations of viscoplastic plates under impulsive loading are compared to each other. The aim is to determine how accurately the measured deformations can be calculated by the chosen constitutive and structural theories. A first‐order shear deformation shell theory assuming small strains and moderate rotations and viscoplastic laws are applied. In the experimental part of this study short time measurement techniques are applied to shock tubes in order to record fast loading processes and plate deformations.  相似文献   

    

G. Rosi  I. Giorgio  V.A. Eremeyev 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2013,93(12):914-927

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, we use a non‐convex 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, with particular attention to the behaviour in correspondence of the interfacial layer. The reflection and transmission of waves is studied and analized with the aid of numerical simulations, and an interesting phenomenon of mass adsorption at the interface is observed and discussed.  相似文献   

    

Eugene Kazantsev 《国际流体数值方法杂志》2011,65(10):1231-1259

A variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near the boundary rather than boundary conditions is shown. Assimilating data that have been produced by the same model on a finer grid, in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under‐resolved boundary layer and wrong wave velocity. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

    

H. Holmås  D. Clamond  H. P. Langtangen 《国际流体数值方法杂志》2008,58(6):639-658

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E. I. Romenskii 《Journal of Applied Mechanics and Technical Physics》2007,48(3):437-444

Constitutive equations that describe the experimentally observed failure waves are proposed to model inelastic strains of brittle materials. The complete system of equations is hyperbolic, each equation of this system has divergent form. The model is based on the assumption that continual failure is the process of transition from an intact state to a “fully damaged” state described by the kinetics of the order parameter. The structure of stationary traveling compressive waves is analyzed using a simplified model. It is shown that in a certain range of amplitudes, the wave splits into an elastic precursor and a failure wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 164–172, May–June, 2007.  相似文献   

    

V. Eremeyev  L. Zubov 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(2):94-101

Constitutive inequalities in general static and dynamic theory of elastic shells undergoing finite deformation are discussed. Constitutive inequalities are well known in continuum mechanics. They express physical or mathematical restrictions for constitutive equations of 3D elastic materials. In this paper we discuss the analogs of the strong ellipticity, Hadamard and Coleman‐Noll (GCN‐condition) inequalities for nonlinear elastic shells. It is shown that the GCN‐condition implies the strong elipticity for shell theory whereas the strong ellipticity is equivalent to the existence conditions of acceleration waves in shell.  相似文献