Time-Harmonic Waves Propagating Normal to the Layers of Multilayered Periodic Media

The dispersion relation is derived for time-harmonic waves propagating normal to the layers of a multilayered periodic composite. The known relations for the homogeneous and the bilaminated media are deduced as special cases. Mixture mass density and elastic modulus are defined in the limit as the ratio of the incident wavelength to the microdimension of the composite approaches infinity.

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Elastic Waves in Inhomogeneous Elastic Media

Journal of Applied Mechanics ◽

10.1115/1.3422775 ◽

1972 ◽

Vol 39 (3) ◽

pp. 696-702 ◽

Cited By ~ 12

Author(s):

Adnan H. Nayfeh ◽

Siavouche Nemat-Nasser

Keyword(s):

Perturbation Method ◽

Incident Wave ◽

Elastic Waves ◽

Harmonic Waves ◽

Elastic Media ◽

Time Harmonic ◽

Special Cases ◽

Inhomogeneous Elastic Media ◽

Inhomogeneous Elastic Medium ◽

Large Frequency

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.

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Time-Harmonic Waves Traveling Obliquely in a Periodically Laminated Medium

Journal of Applied Mechanics ◽

10.1115/1.3408800 ◽

1971 ◽

Vol 38 (2) ◽

pp. 477-482 ◽

Cited By ~ 38

Author(s):

C. Sve

Keyword(s):

Dispersion Relation ◽

Fourth Order ◽

Continuum Theory ◽

Numerical Results ◽

Harmonic Waves ◽

Two Dimensional ◽

Arbitrary Direction ◽

Arbitrary Angle ◽

Phase Velocities ◽

Time Harmonic

The dispersion relation is presented for time-harmonic waves propagating in an arbitrary direction in a periodically laminated medium. The analysis is based on two-dimensional equations of elasticity. Limiting phase velocities are presented for infinite wavelength for any angle of propagation in the form of a fourth-order determinant that illustrates the influence of an arbitrary angle. For the cases when the propagation is along or across the layers, the determinant reduces to two determinants of second order that yield the limiting phase velocities directly. Numerical results are presented to indicate the dependence of dispersion upon the angle of propagation. Also, a comparison with an approximate continuum theory is included; agreement is satisfactory for those angles where the dispersion is the strongest.

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Dynamic Equivalence of Composite Material and Eigenstrain Problems

Journal of Applied Mechanics ◽

10.1115/1.3423012 ◽

1973 ◽

Vol 40 (2) ◽

pp. 498-502 ◽

Cited By ~ 10

Author(s):

P. Wheeler ◽

T. Mura

Keyword(s):

Composite Material ◽

Variational Formulation ◽

Necessary Conditions ◽

Mode Shapes ◽

Homogeneous Material ◽

Harmonic Waves ◽

Dynamic Equivalence ◽

Displacement Mode ◽

Time Harmonic ◽

Special Cases

The variational method is employed for determining the displacement mode shapes and dispersion relations for the problem of plane time-harmonic waves propagating through an infinitely extended, periodically arranged composite material. Numerical results are obtained for the special cases of laminated and fiber-reinforced media. Using variational formulation, the composite problem is compared with the problem of a homogeneous material subjected to eigenstrain and body forces. Necessary conditions are developed for the dynamic equivalency of the two problems. Distributions of eigenstrain are shown which yield the same displacement solutions as the problem of a transverse wave propagating normal to the layers of a laminated media.

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Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

Communications in Computational Physics ◽

10.4208/cicp.231109.090710s ◽

2012 ◽

Vol 11 (2) ◽

pp. 303-318 ◽

Cited By ~ 2

Author(s):

J. Coatléven ◽

P. Joly

Keyword(s):

Multiple Scattering ◽

Random Number ◽

Good Method ◽

Computational Domain ◽

Periodic Media ◽

Scattering Problems ◽

Compact Perturbations ◽

Time Harmonic ◽

Operator Factorization ◽

Interior Problem

AbstractThis work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

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Time Harmonic Waves in Elastic Waveguides

The Theory of Elastic Waves and Waveguides - North-Holland Series in Applied Mathematics and Mechanics ◽

10.1016/b978-0-444-87513-6.50010-8 ◽

1978 ◽

pp. 178-230

Keyword(s):

Harmonic Waves ◽

Time Harmonic ◽

Elastic Waveguides

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Inverse Scattering Theory for Time-Harmonic Waves

Lecture Notes in Computational Science and Engineering - Topics in Computational Wave Propagation ◽

10.1007/978-3-642-55483-4_9 ◽

2003 ◽

pp. 337-365 ◽

Cited By ~ 1

Author(s):

Andreas Kirsch

Keyword(s):

Inverse Scattering ◽

Scattering Theory ◽

Harmonic Waves ◽

Time Harmonic ◽

Inverse Scattering Theory

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Jeans instability in non-minimal matter-curvature coupling gravity

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8189-y ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

Cláudio Gomes

Keyword(s):

Boltzmann Equation ◽

Dispersion Relation ◽

Weak Field ◽

Model Parameters ◽

Field Limit ◽

Modified Dispersion Relation ◽

Weak Field Limit ◽

Special Cases ◽

Jeans Instability ◽

Scalar Potentials

Abstract The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean’s criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.

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Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

Journal of Plasma Physics ◽

10.1017/s002237781800020x ◽

2018 ◽

Vol 84 (2) ◽

Cited By ~ 5

Author(s):

Daniele Brunetti ◽

J. P. Graves ◽

E. Lazzaro ◽

A. Mariani ◽

S. Nowak ◽

...

Keyword(s):

Dispersion Relation ◽

Safety Factor ◽

Mass Density ◽

Analytic Study ◽

Pressure Gradients ◽

Plasma Edge ◽

Vacuum Region ◽

Metallic Wall ◽

Equilibrium Profiles ◽

Pressure Driven

The problem of pressure driven infernal type perturbations near the plasma edge is addressed analytically for a circular limited tokamak configuration which presents an edge flattened safety factor. The plasma is separated from a metallic wall, either ideally conducting or resistive, by a vacuum region. The dispersion relation for such types of instabilities is derived and discussed for two classes of equilibrium profiles for pressure and mass density.

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