Counter-propagation of harmonic waves in exponentially graded materials

Counter-propagation and interaction of two ultrasonic harmonic waves in strongly inhomogeneous exponentially graded material is studied. Deformations of a specimen with two parallel boundaries are described by the five-constant nonlinear theory of elasticity. One-dimensional problems are investigated in detail. The influence of material properties variation on the profile of boundary oscillations is clarified. The obtained results will be useful in ultrasonic nondestructive material characterization.     

Generalized thermoelastic waves in homogeneous isotropic plates

The propagation of thermoelastic waves in homogeneous isotropic plate subjected to stress-free and rigid insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS), Green-Lindsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. It is shown that the motion for SH modes gets decoupled from the rest of the motion and remains unaffected due to thermo-mechanical coupling and thermal relaxation effects. The phase velocities for SH modes have also been obtained. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. At short wavelength limits the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and isothermal plate reduce to Rayleigh surface waves frequency equations. Finally, the numerical solution is carried out for aluminum-epoxy composite material and the dispersion curves for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.     

Plane waves in noncommutative fluids

We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy–momentum tensor of the plane waves is calculated.     

Excitations of thermoelastic waves in plates by a pulsed laser

The method of the eigenfunction expansion, also known as the expansion in normal modes, is employed to study numerically the axisymmetric excitation of the thermoelastic waves in plates by a pulsed laser. This method gives a systematic treatment and allows one to investigate not only the quasistatic and dynamic thermoelastic responses of pulsed photothermal deformation on the time scale of 1 s, but also the thermoelastic generation of longitudinal, transverse, and surface acoustic waves in thick materials, as well as the excitations of the Rayleigh-Lamb wave modes in thin plates. The formalism is particularly suitable for waveform analyses of the excitations of transient Lamb waves in thin plates because one needs only to calculate the contributions of several lower eigenmodes. The numerical technique provides a quantitative tool for the experimental determination of material properties, especially the mechanical and elastic properties of free-standing films and thicker sheet materials by thermoelastic detection.     

Laser-generated thermoelastic acoustic sources and Lamb waves in anisotropic plates

The effect of anisotropy and temperature on the dispersive Lamb wave generation and propagation in a transversely isotropic thin plate has been investigated. A quantitative numerical model for the laser-generated transient ultrasonic Lamb waves propagating along arbitrary directions is presented by using a finite-element method. All factors, such as spatial and time distributions of the incident laser beam, optical penetration, thermal diffusivity, thickness of the plate, and source–receiver distance, can be taken into account. The effects on the ultrasound waveform of the size of the optoacoustic source are investigated; in the limit of strong optical absorption, a subsurface thermal source gives rise to both vertical and lateral shear tensions. The lateral shear tension is equivalent to applying a shear dipole at the top face; the amplitude of the dipole is a function of material symmetry, contrary to the isotropic case, and the character and strength of the equivalent surface stress are a function of propagation direction. The specific results for the lower anti-symmetric and symmetric mode propagation in all planar directions are presented in the thermoelastic regime; the spatial dispersion (variation of the velocity with the direction of propagation) as well as the frequency dispersion is analyzed. PACS 43.35.+d; 02.70.Dh; 42.62.-b; 78.20.Nv; 81.70.Cv     

Plane and cylindrical shock waves in magnetogasdynamics

Summary The Chisnell-Chester-Whitham method has been used to study the propagation of diverging plane and cylindrical shock waves through an ideal gas in the presence of a magnetic field having only constant axial and azimuthal components, simultaneously for both weak and strong cases. By assuming an initial density distribution ϱ₀ = ϱ′r ^−W , where ϱ′ is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density and the particle velocity immediately behind the shock have been derived for both the cases.

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Riassunto Il metodo di Chisnell-Chester-Whitham è stato usato per studiare la propagazione di onde d’urto divergenti cilindriche e piane attraverso un gas ideale in presenza di un campo magnetico che ha solo componenti costanti assiali e azimutali, contemporaneamente per casi deboli e forti. Assumendo una distribuzione di densità iniziale ϱ₀ = ϱ′r ^−W , dove ϱ′ è la densità al piano/asse di simmetria ew è una costante, si sono ottenute le espressioni analitiche per la velocità d’urto e la forza d’urto. Le espressioni per la pressione, la densità e la velocità delle particelle immediatamente dopo l’urto sono state determinate per entrambi i casi.

     

Plane waves in gauge theories of gravitation

Exact solutions representing pp waves are found in a wide class of gauge theories of gravitation. Algebraic and symmetry properties are investigated and a special case of plane waves is discussed.The work reported in this paper was carried out as part of the Polish Research Project MR-I-7.     

Plane waves in the bimetric gravitation theory

Field equations for plane waves are set up and some solutions are obtained. Transverse, longitudinal, and mixed waves are possible. In the purely transverse case the energy density is positive definite. In the purely longitudinal case it may be negative. However, in one example investigated it is positive if the Riemannian metric tensor satisfies a condition corresponding to space-time having satisfactory physical properties.     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

Conical harmonic generation in isotropic materials

A novel class of nonlinear optical processes is described in which radiation at the nth harmonic is generated through the use of a (2n+1)-order nonlinearity. Utilizing an odd-order nonlinearity, this process allows for the generation and amplification of both odd- and even-order harmonics in isotropic materials. Additionally, this process can always be phase matched in normal-dispersion materials without the use of birefringence. Experimental results are presented in which conical third-harmonic emission is generated from a sapphire sample.     

Dissipative properties of materials with thermoelastic martensite conversion

Conclusion Internal friction in metallic materials experiencing a thermoelastic martensite conversion under conditions of a monotonically changing thermodynamic stimulus is determined by two main factors: irreversible processes involving growth of crystals of the new phase, and cyclical motion of the phase boundaries under the action of applied periodic stresses. While the losses caused by irreversible processes decrease with increase in loading amplitude, depending on the type of conversion the amplitude dependence of the background component of internal friction may be of a complex nonmonotonic character, with a maximum in losses at certain oscillation amplitudes. At low amplitudes sections of the boundary unattached to defects perform cyclical motions like membranes, and the losses due to the thermal conversion effect may produce a significant contribution to the overall damping level only at the membrane resonant frequencies. For amplitudes exceeding the critical boundary detachment stress internal friction increases, passes through a maximum, and then decreases anew. The amplitude dependence of internal friction behaves in a similar manner in the process of creation and subsequent collapse of crystals of the new phase in the field of an external periodic load.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 54–67, May, 1985.     

Plane waves in effective field theories of superstrings

Exact plane wave solutions of d = 10, N = 1 Einstein-Yang-Mills supergravity theory are presented and their possible modifications in superstring effective theories are examined. It is found that the solutions are not affected by any of the known heterotic string corrections. It is argued that plane waves satisfy the effective field equations of the heterotic string theory in all powers of the string tension parameter α′, possibly after including a totally antisymmetric torsion field and reinterpreting the constants. Similar remarks also apply for type I superstrings. Further properties of the solutions are discussed.     

Plane waves in the general theory of relativity

The Newman-Penrose method is used to study the class of gravitational fields in a vacuum which permit a normal congruence of isotropic geodesies. The energy-momentum tensor is used in tetrad form to prove that if the nondegeneratemetric of these fields depends only on a single isotropic coordinate, the solutions will describe plane gravitational waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 20–23, April, 1969.     

Damped cyclotron harmonic waves at oblique propagation

The dispersion relation of CHW at oblique propagation in a wave magenetoplasma exhibits many damped roots between two successive cyclotron harmonics. The two less damped are those obtained by Tataronis and Crawford.     

X waves generated at the second harmonic

The process of optical frequency doubling in the undepleted regime can lead to the generation of an X-wave envelope with group velocity locked to the pump beam. Its parameters and its angular spectrum are directly related to the zeroth- and first-order dispersive features of the nonlinear process. This constitutes a novel mechanism for spatiotemporal localization of light.     

Generation of cyclotron harmonic waves in the ionosphericmodification experiments

In the present paper, the parametric decay instability of the pump X-mode into electron Bernstein wave (EBW) near second harmonics of electron cyclotron frequency and IBW at different harmonics (ωci; n=2,3,4) is examined. Expressions are derived for homogenous threshold, growth rate and convective threshold for this instability. Applications and relevances of the present investigation to ionospheric modification experiment in the F-layer of the ionosphere as well as during intense electron cyclotron resonance heating in the upcoming MTX tokamak have been given     

Laser-induced thermoelastic Leaky Lamb waves at the fluid–solid interface

A model based on the theory of fluid–structure interaction is developed to simulate the laser thermoelastic generation and propagation of Leaky Lamb waves at the water–aluminum interface. Each component of displacement, stress, and temperature are derived in transform domain by the photothermoelastic transfer matrix method. The time domain solutions are obtained by numerically inverting the transforms while the dispersion curves and attenuation curves for the leaky waves are also calculated. Then the propagation characteristics of different modes are analyzed. The model establishes a quantitative relation between the laser parameters, the material parameters, the corresponding waveforms, and the dispersion curves, which provides a useful tool for the Leaky Lamb waves applied to nondestructive evaluation.     

The thermoelastic excitation of air-solid interface waves using the pulsed laser

In the 1920s, the solid-solid interface wave, Stoneley wave, was first studied by Stoneley. From the 1930s to 1940s, the fluid-solid interface waves, usually called Scholte wave or Scholte-Stoneley wave, were studied by Cagniard and Scholte respec-tively[1]. The Scholte wave corresponds to the real root of the fluid-solid interface secu-lar equation, which is usually called the Scholte equation, and the velocity of Scholte wave is only slightly lower than the longitudinal velocity of the f…