Nonlinear theory of the compressible gas flows over a nonuniform boundary in the gravitational field in the shallow-water approximation

A set of equations is derived for the motion of a compressible ideal gas over a nonuniform boundary in the gravitational field in the shallow-water approximation. Classical simple waves are shown not to be the solutions to this set of equations. Generalized simple waves are found to exist only in the case of a linear underlying-surface profile. All continuous and discontinuous solutions are obtained in an explicit form for the case of the boundary in the form of an inclined plane, and an analytical solution is found for the problem of the decay of an arbitrary discontinuity. This solution consists of four wave configurations. Necessary and sufficient conditions are determined for the existence of each configuration.     

Wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section

In this paper, the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non-extensible membranes. The three-dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations, which relate the frequencies of elastic waves to their wavenumbers. Numerical results for waveguides with various boundary conditions are presented to illustrate the approach. Analysis of the dispersion spectra is carried out, and cutoff frequencies are obtained and characterized; mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed. The main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed. The results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder.     

Boundary element method for bandgap computation of photonic crystals

A boundary element method for computing bandgap structures of two-dimensional photonic crystals is developed. For photonic crystals composed of a square or triangular lattice of parallel cylinders with arbitrarily shaped cross-sections, the boundary integral equations are formulated for a unit cell. Constant boundary elements are adopted to discretize the boundaries. Applying the periodic boundary conditions and the interface conditions, we obtain a linear eigenvalue equation with relatively small matrices. The solution of the eigenvalue equation yields the Bloch wave vectors for given frequencies. The convergence of the method for the desired accuracy and efficiency is examined by some typical numerical examples. It is shown that the present method is efficient and accurate and thus provides a flexible treatment of electromagnetic waves in periodic structures with inclusions of arbitrary shape.     

The evaluation of non-reflecting boundary conditions for duct acoustic computation

A simple method is used to quantify the performance of non-reflecting boundary conditions for duct acoustic applications. The method uses a two-dimensional wavesplitting technique to decompose the linearized Euler equations into its constitutive modes, allowing the magnitude of reflected waves from outflow boundaries to be accurately determined. Realistic conditions are simulated by conducting the boundary condition analysis using acoustic waves with characteristics often found in duct and turbomachinery problems. For this paper, the method is used to investigate the performance of three different buffer zone implementations and the Perfectly Matched Layer as non-reflecting boundary conditions. The effect of the damping properties of these boundary conditions and the incident acoustic wave characteristics on performance are considered. Results indicate that the buffer zone boundary condition using explicit damping of the solution vector after each timestep produces the best non-reflecting performance. A deterioration in performance was observed for incident waves at high angles relative to the boundary normal for all implementations.     

Acoustic boundary layer

On the basis of the boundary-layer concept, a method is proposed for calculating the oscillation-velocity and temperature fields in a volume of arbitrary form, bounded by rigid walls and filled by a viscous heat-conducting fluid. It is shown that the potential part of the sound field may be determined as in an ideal non-heat-conducting fluid, while close to the wall there are not only potential waves but also eddy velocity waves and temperature waves moving out from the wall. A method of solving a broad class of problems is discussed in which the boundary conditions at a distorted surface may be replaced, without significant error, by conditions at a plane boundary.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 92–97, November, 1980.It remains to thank our colleagues in the acoustics faculty for participating in discussions of the work.     

Propagation of acoustic waves in a medium with the Rayleigh energy release mechanism

This research continues theoretical studies of propagation of acoustic waves in a plasma considering it in the context of a Rayleigh medium. For the first time, the solution to the problem with the boundary and not the initial conditions is examined. It is shown that for small values of the parameter characterizing the energy input in the plasma, the amplification coefficients of a harmonic acoustic wave in the problem of propagation of the initial perturbation and in the problem with the boundary conditions are close. However, if the energy input increases, the amplification of the wave propagating from the source is larger than in the problem of the initial perturbation propagation. The same concerns the amplification of waves with different frequencies for fixed parameters of the plasma; i.e., the difference between the amplification coefficients is larger, the lower the wave frequency. The resultant analytic dependences make it possible to determine exactly which of the problems (with the initial or boundary conditions) should be solved to compute the amplification coefficient of acoustic waves under specific experimental conditions.     

An application of one-sided Jacobi polynomials for spectral modeling of vector fields in polar coordinates

A spectral tau-method is proposed for solving vector field equations defined in polar coordinates. The method employs one-sided Jacobi polynomials as radial expansion functions and Fourier exponentials as azimuthal expansion functions. All the regularity requirements of the vector field at the origin and the physical boundary conditions at a circumferential boundary are exactly satisfied by adjusting the additional tau-coefficients of the radial expansion polynomials of the highest order. The proposed method is applied to linear and nonlinear-dispersive time evolution equations of hyperbolic-type describing internal Kelvin and Poincaré waves in a shallow, stratified lake on a rotating plane.     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

Seismic scattering from a spherical inclusion eccentrically located within a homogeneous,spherical host: theoretical derivation

Abstract

The scattered fields from a spherical body eccentrically located within an otherwise homogeneous host sphere are derived by satisfying the boundary conditions at both interfaces simultaneously. The source, which may be composed of any linear combination of S and P waves, is also located arbitrarily within the host sphere. The scattering system may have applications in seismic scattering, by cavities or dense bodies located near the Earth surface or to the Slichter mode.     

Propagation of electromagnetic waves through very thin non-Hermitian slabs

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes with a Kerr-type nonlinearity. A number of relations between the real and imaginary parts of the dielectric function are derived in order that useful effects related to the non-Hermiticity of the system be presented. The transmission of plane waves through a system consisting of two thin slabs satisfying the condition of Parity-Time symmetry is also considered.     

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.     

Plumes and waves in two-dimensional turbulent thermal convection

We have conducted a high-resolution, two-dimensional direct numerical simulation of Rayleigh-Bénard convection with stress-free and periodic boundary conditions at a Rayleigh (Ra) number of 10(8) and Prandtl (Pr) number of unity. An aspect-ratio three box has been considered. A single cell has been used as the initial condition. First, the flow develops into time-dependent convection with a strong asymmetry and highly convoluted thermal plumes delineating a large-scale circulation. Smaller thermal plumes detach from the boundary layer and extend over the entire cell, creating a local inversion of the temperature gradient adjacent to the boundary layers. Then the conditions leading to the formation of internal waves are fulfilled, as the local Richardson number decreases sufficiently small to cross the linear threshold of Ri=0.25. Together with the strong shear, convective rolls with a Kelvin-Helmholtz wavelike character are produced. The secondary boundary layer itself becomes unstable and produces smaller plumes. At later times, the large-scale circulation is destroyed and the internal waves disappear. A Reynolds number, based on the global scale, of Re=500, is attained at this stage. Only isolated thermal plumes and vortices are present. Thus, internal waves can be generated at finite Prandtl number fluids for sufficiently high Ra in the presence of a large-scale circulation. Spectral analysis reveals that the kinetic energy decays with a logarithmic slope of -3, while the logarithmic slope of the thermal variance has a value of around -5 / 3.     

Stability of supersonic boundary layer on a porous plate with a flexible coating

The development of disturbances in the boundary layer of compressible gas on a flexible surface has been investigated in the linear and nonlinear approximations (the weakly nonlinear stability theory). The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities as well as a model of a porous wall, on which a flexible film is spanned, have been considered. The boundary conditions for disturbances with regard for their transformation by a flexible porous coating have been derived. The character of the variation of the coefficients of the stream-wise growth of linear oscillations of different nature (the vortex waves of the first mode and the acoustic waves of the second mode) is shown. The direction and the degree of their deformations are determined by the flexible coating parameters. It is found that at moderate Mach numbers, the stabilization of disturbances and the diminution of increments occur, whereas at high M on a surface with a film, the acoustic components are destabilized, which may lead to an earlier onset of nonlinear processes. The nonlinear interactions in three-wave symmetric triplets between the vortex waves at M = 2 and between the waves of different nature at M = 5.35 are considered. In the latter case, the plane acoustic wave is the pumping wave, which excites the three-dimensional subharmonic components of vortex nature.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

Study of the influence of thin layer loading on the propagation of Lamb waves using perturbation method

I.IntroductionSincethepublicationoftheclassicalpaper"Onthewavesinanelasticplate"byH.Lambin1917l1l,theterm"LaInbwave"hasbeenusedtorefertoanelasticdisturbancepropagatinginasolidplatewithfreeboundaries.Lambwavesarewidelyusedintheapplicationsofthedefectinspectionofthinwa.lledmaterial[2'8].InrecelltyearsLambwaveshavebeenwide1yusedinthefabricationofsensors.LamInwavesensorsdetectthechangesofenvironmentbymeasuringthechangeofphasevelocityofLambwaves.IncomparisonwithbuIkwavesandSAW's,Lambwavsprovi…     

Seismic scattering from a spherical inclusion eccentrically located within a homogeneous, spherical host: theoretical derivation

The scattered fields from a spherical body eccentrically located within an otherwise homogeneous host sphere are derived by satisfying the boundary conditions at both interfaces simultaneously. The source, which may be composed of any linear combination of S and P waves, is also located arbitrarily within the host sphere. The scattering system may have applications in seismic scattering, by cavities or dense bodies located near the Earth surface or to the Slichter mode.     

Nonlinear acoustic scattering by a partially closed surface-breaking crack

A theoretical model describing the nonlinear scattering of acoustic waves by surface-breaking cracks with faces in partial contact is presented. The nonlinear properties of the crack are accounted for by suitable boundary conditions that are derived from micromechanical models of the dynamics of elastic rough surfaces in contact. Both linear and nonlinear responses of the crack are shown to be largest for a shear vertical wave incident on the surface containing the crack at an angle just above the critical angle for longitudinal waves. These findings question the fitness for the purpose of a conventional inspection method, which utilizes shear vertical waves at 45 degrees of incidence to search for surface-breaking cracks in many engineering components. For angles of incidence proximal to the critical angle of longitudinal waves, the efficiency of the second harmonic's generation appears to be the highest. Thanks to the increased sensitivity to surface-breaking cracks, this configuration seems to offer a solution to the localization problem, a task that has eluded nonlinear techniques operating under other circumstances. Finally, this model suggests a simple interpretation of the highly localized nonlinear response of delaminations in composite materials.     

Hydroelastic interaction between water waves and a thin elastic plate of arbitrary geometry

An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered reg...     

Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

We investigate the dynamical behaviour of a coupled dispersionless system （CDS） by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most conditions. stable travelling waves in another situation of boundary conditions.     

Reflexion und Brechung des Lichtes an einer anisotropen Schicht

Reflection and Refraction of Light by an Anisotropic Layer The linear problem of reflection and refraction of plane monochromatic electromagnetic waves by a plane-parallel homogeneous anisotropic layer between (in general different) homogeneous optically isotropic semiinfinite media is treated on the basis of MAXWELL 's equations and the boundary conditions following from them. The permittivity tensor of the anisotropic layer is assumed to be widely arbitrary and therefore asymmetric, neglecting only the spatial dispersion, i. e., the dependence on the wave vector. The electrical fields of reflected, refracted, and transmitted waves are calculated in dependence on the electric field of the incident wave. The conditions for waveguide modes of the layer in the absence of incident waves are obtained from the vanishing of a determinant. The general formulae are specialized to the cases of normal incidence and also of perpendicular and parallel polarisation, relatively to the plane of incidence, of the refracted partial waves in the anisotropic layer thus obtaining simplifications in these cases. The interesting cases of uniaxial layers, when the optic axis lies either parallel or perpendicular to the plane of incidence, belong to the last mentioned special cases of perpendicular and parallel polarisation relatively to the plane of incidence.