Problem Of Wave Reflection Research Articles

Dynamic Stiffness of Cracked Interfaces

Quantitative relationships are derived between the dynamic macromechanical stiffness and microparameters of planar interfaces containing distributed cracks. The derivation is based on the solution of the problem of elastic wave reflection by a plane with a continuous distribution of springs to model the cracked interface at the macrolevel. The dynamic spring stiffness is then, through averaging, related to crack-opening volumes and other microparameters. For linear springs and periodic crack distributions, numerical examples are presented for plain strain. The stiffness is shown to strongly depend on frequency.

Boundary element calculation of shallow water waves

A boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.

On the general problem of Kelvin wave reflection at an oscillating boundary

The author's (1987) model of Kelvin wave reflection at an oscillating boundary is reformulated to allow an arbitrary specification of the amplitude and phase of the boundary oscillation relative to the incoming wave. Solutions are obtained numerically by the method of collocation and imperfect reflection is found to occur in general, in agreement with the author's theory. It is shown that there are three regimes of solutions characterized by the size of the boundary oscillation. In view of the present interest in the North Sea (NERC Community Research Project) it is hoped that this first-order theory can give some insight into the basic tidal behaviour of the North Sea from which more realistic models can be developed.

A comprehensive analysis of surface acoustic wave reflections

A thorough study of the perturbative and variational approaches is carried out for the surface acoustic wave reflection problem. We have shown that the perturbation treatment by Datta and Hunsinger and potentially powerful variational formulation by Chen and Haus [IEEE Trans. Sonics Ultrason. SU-32, 395 (1985)] are mutually consistent. In their common region of validity, these two approaches yield nearly identical results for the reflection coefficients and velocity shifts due to metal finger and groove overlays. Term-by-term comparison of the mass- and stress-loading effects, and also the electric shorting effect, is carried out to provide a coherent picture of the reflection phenomena. The on- and off-resonance behavior of the reflection coefficient can be described correctly using either one of these theories, with proper inclusion of the overlay shape dependence. A new term for electric shorting is derived for groove overlays.

The Exciton Reflection Shifting and Modification in Presence of Intensive Polariton Wave Interacting with LO‐Phonons in Polar Semiconductors

AbstractA set of macroscopic phonoriton equations describing exciton, photon, and LO‐phonon spectra renormalization in presence of intensive polariton wave is analyzed. New specific additional boundary conditions are introduced and corresponding exciton reflection spectra are calculated for the problem of probe wave reflection at the crystal boundary. The appearance of the new phonoriton spike and the exciton line shifting in reflection spectra are determined by the intensity of the pumping wave.

Wave reflection from a system of plane layers

A method for dealing with the interface problem of wave reflection and refraction through a layered-homogeneous and non-absorbing medium is developed, for an arbitrary (not necessarily periodic) TE or TM electromagnetic wave at non-crirical incidence. The problem is reduced to solving a functional equation for one of the Riemann invariants, under a suitable restriction on the reflection coefficients of the layers and the angle of incidence. Conditions for no reflection in the periodic case are found, thus extending known results for time-harmonic waves in the framework of the theory of optical reflection-reducing layers.

The viscoelastic reflection/transmission problem: Two special cases

AbstractIn the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

Over-reflection and instability

Stability problems involving parallel shear flow are considered in the context of wave-reflection problems. It is found that if an unstable solution exists and its growth rate is sufficiently small, the growth rate can be connected to the reflection coefficient through a formula as if the unstable growth were the direct result of repeated over-reflections. If the stability problem under consideration has time symmetry, then for every growing solution there exists a corresponding decaying solution. It is shown that a consistent formula can also be derived for the decaying solution, and the existence of at least one critical layer in the corresponding wave-reflection problem is needed in order to account for both the growing and decaying solutions. As an application of these concepts, the small-scale non-geostrophic instabilities found by Stone (1970) are identified to be associated with over-reflection of inertia-gravity waves.

A Coordinate-Free Approach to Wave Reflection from a Uniaxially Anisotropic Medium

This paper presents a coordinate-free method of solving the problem of electromagnetic wave reflection from the surface of a uniaxially anisotropic medium. Based on the direct manipulation of vectors, dyadics, and their invariants, the method eliminates the use of coordinate systems. It facilitates solutions and provides results in a greater generality. The paper contains the following results in coordinate-free forms: a) the dispersion equations; b) me directions of field vectors; c) the Poynting vectors (ray vectors) and group velocities d) the' laws of reflection and refraction; and e) the transmition and reflection coefficients. The results are valid for the incident wave having any polarization, and the optic axis of the uniaxial medium being arbitrarily oriented with respect to the interface and the plane of incidence.

On regular reflection of a shock wave from a rigid wall

The three-dimensional problem of reflection of a shock wave of arbitrary front shape from a fixed rigid wall is considered. Existence of a piecewise analytic solution of the problem defining the initial stage of regular reflection is proved. Expansion of solution behind the reflected wave front in converging power series in the neighborhood of the incident wave (of the moving along the wall intersection line of the incident wave front and the rigid wall) is obtained for prolonged instants of time. It is shown that such expansions generally occur only then, when the length of the trace velocity vector relative to gas behind the reflected wave projected on the plane normal to the trace exceeds the speed of sound. A bibliography of publications dealing with the problem of shock wave reflection can be found in /1,2/.

Electromagnetic spherical wave reflection from a perfectly conducting surface of revolution

The problem of electromagnetic spherical wave reflection from a perfectly conducting surface of revolution is considered. The expressions for the first two terms of the high frequency asymptotic expansion for the reflected field are found. The analysis is based on Lee's theory of electromagnetic reflection from a conducting surface.

A coordinate‐free approach to wave reflection from an anisotropic medium

The object of this paper is to present a coordinate‐free method in solving the problem of wave reflection from the surface of an anisotropic medium. Based on the direct manipulation of vectors, dyadics, and their invariants, the method eliminates the use of coordinate systems. It facilitates solutions and provides results in a greater generality. The paper contains the following results in coordinate‐free forms: (1) the dispersion equation, (2) the laws of reflection and refraction, (3) the Booker quartic equation, and (4) the transmission and reflection coefficient matrices.

Interaction of interplanetary shock waves with the bow shock‐magnetopause system

The collision of interplanetary shock waves with the bow shock wave‐magnetopause system is considered both in the gas‐dynamic and magnetohydrodynamic approximations. It is shown that the shock wave is reflected from the magnetopause as a rarefaction wave which, in turn, is reflected from the rearward side of the bow shock. This secondary rarefaction wave arrives at the magnetosphere after a time interval of 3–5 min after the interplanetary shock wave's arrival. The rarefaction wave decreases the flow pressure on the magnetosphere and causes the reverse (i.e., outward) motion of the magnetopause. With the help of an approximate solution of the differential equations the problem of rarefaction wave reflection from the magnetosphere is considered. The law of the subsolar point motion of the magnetosphere during the abrupt shock‐like perturbation is obtained. The experimental data confirm the theoretical results.

The existence of Stoneley waves as a loss mechanism in plane wave reflection problems

In a previous paper [’’Influence of Stoneley waves on plane-wave reflection coefficients: Characteristics of bottom reflection loss,’’ K. E. Hawker, J. Acoust. Soc. Am. 64, 548 (1978)] it was shown that for certain configurations of layered fluids overlying a rigid (solid) substrate, the reflection loss would display narrow peaks of significant amplitude. It was suggested in that paper that these peaks were due to excitation of Stoneley waves at the fluid–solid interface. In the present paper this association is made more precise and definite. Through an extension of the classical theory of Stoneley waves to the case of inhomogeneous media, it is shown that the angles at which the reflection-loss peaks occur are precisely those angles for which the horizontal component of phase velocity in the fluid equals the Stoneley wave phase velocity. In addition, the near independence of the reflection loss peaks on frequency is explained quantitatively.

Reflection of a Gaussian ultrasonic beam from Al2O3 layer–stainless steel in water at the Rayleigh angle

The problem of ultrasonic wave reflection at a Rayleigh angle from Al2O3 layer–stainless steel in water was investigated. The so-called leaky Rayleigh velocity was measured by using an optical schlieren technique to identify the Rayleigh angle. The magnitude of the measured leaky Rayleigh velocity for the coated surface is smaller than the corresponding leaky Rayleigh velocity for either stainless steel or for Al2O3.

Over−reflection of horizontally propagating gravity waves by a vertical shear layer

The problem of horizontally propagating gravity waves impinging on a vertical shear layer which forms the boundary between uniform currents is isomorphic to an acoustic problem solved by Miles and by Ribner. The consequences of over‐reflection for a spatially growing instability are pointed out. The long wave reflection problem is solved for free surface and internal waves on a thin layer in an otherwise deep fluid. Over‐reflection is found possible for Froude numbers in excess of two; infinite over‐reflection will occur for certain angles of impingement.

Reflection and refraction of an obliquely incident electromagnetic wave interacting with a moving, magnetized plasma slab

The problem of wave reflection and refraction at a moving magnetized plasma slab has been treated for arbitrary angles of incidence. The external magnetic field has been taken normal to both the plane of incidence and the direction of motion of the slab. Expressions are obtained for the phase shifts and the power reflection and transmission coefficients for both an incident E-wave and an incident H-wave. It is found that as against the case of a moving magnetized or unmagnetized plasma half-space, there is a finite transmission through the plasma slab at a cut-off point (kpe = 0). Further, for a moving plasma slab some unique Brewster's angles are shown to exist. For an isotropic plasma slab, in particular, the Brewster's angles are independent of the velocity of the slab medium and exist only for plasma frequencies less than the signal frequency (ωp < ω). In addition, the various reflection and refraction properties for an incident E-wave turn out to be independent of magnetic field strength and the velo...

Nonquasineutral theory of ion-acoustic resonances in bounded nonuniform plasmas and comparison with experiments

A theory is developed of ion-acoustic resonances in inhomogeneous plasmas of the positive column type using a fluid plasma description. Poisson's equation is properly taken into account, instead of applying the usual assumption of wave quasineutrality. The order of the differential equation describing the wave is thereby increased by two and the singularity that previously occurred as a result of the presence of a sheath region is thereby removed. It is shown that ion-acoustic resonances are confined within the plasma core, the effective boundary not being the wall, but the region in the plasma where the macroscopic ion flow velocity attains the Bohm velocity (KTe/mi)(1/2). The theoretical predictions are substantiated by a number of experiments taken from the literature and supplemented by a series of new experiments. The theory sheds new light on the problem of wave reflection from a negatively polarized wall and the damping of ion-acoustic waves propagating in inhomogeneous plasmas.

Guided Surface Waves on an Elastic Half Space

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Transmission-Line Analogies of Plane Electromagnetic-Wave Reflections

The similarity between the equations for unguided plane electromagnetic-wave propagation and those of propagation along conventional transmission lines is illustrated here. It is shown that the conventional transmission-line equations expressed in terms of receiving-end voltage and current may be used to express the field-intensity components of uniform plane waves in any medium. Normal-incidence reflection of plane waves at surfaces of discontinuity are shown to be analogous to transmission-line reflections at impedance discontinuities. The transmission-line equations are then modified to apply to oblique incidence reflection. The relationships developed here assist in visualizing as well as solving plane-wave propagation and reflection problems using the conventional transmission-line equations. It also makes possible the use of transmission-line charts for the solution of wave-reflection problems.