On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space

In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a first-order linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the first-order differential system follows. On this basis, the Rayleigh-type surface waves are studied, and the dispersion condition is found.     

Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model

The present paper deals with the study of Rayleigh waves in a thermoelastic homogeneous isotropic solid half space in the context of dual-phase-lag model. The medium is subjected to stress free, thermally insulated, boundary conditions. The equation for the phase velocity of Rayleigh waves and the analytical expressions for the amplitudes of the displacements, temperature and thermal stresses have been derived. The expressions are obtained for a wave traveling along the free surface. The results discussed numerically and illustrated graphically to show effect of the coupling parameter and phase-lags.     

Rayleigh waves at the boundary surface of modified couple stress generalized thermoelastic with mass diffusion

In this problem, we have studied propagation of Rayleigh waves in an homogeneous isotropic modified couple stress generalized thermoelastic with mass diffusion solid half space in the context of Lord–Shulman (L-S), Green–Lindsay (G-L) theories of thermoelasticity. Secular equations are derived mathematically by using appropriate boundary conditions. The values of determinant of secular equation, Rayleigh wave velocity and attenuation coefficient with respect to angular velocity for different values of wave number and relaxation times in the absence and presence of mass diffusion, are computed numerically. The numerical simulated results are depicted graphically for copper material.     

Nonstationary heat conductivity of moist bodies

The temperature field of moist bodies in the form of a plate, a hollow cylinder, and a hollow sphere is analyzed for general boundary conditions of the third kind at the inner and outer surfaces.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 6, pp. 1067–1073, December, 1968.     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Similarity prediction of wall jets on bodies of revolution

Summary The problem of turbulent wall jets on bodies of revolution is investigated by means of a similarity analysis. The procedure aims to determine functional dependence of mean flow similarity scales (length and velocity scales) on a shape parameter. Discussion dealing with the applicability of the obtained results is carried out with reference to previously published ones cited in the literature. With 5 Figures     

Interaction of a combination of bodies in supersonic flow. Interference and diffraction of shock waves in flow over two bodies of revolution

Results are presented of numerical investigations of three-dimensional supersonic flows in a disturbed region of jointly streamlined two identical bodies arranged in parallel which represent combinations of a cone with a semivertex angle of 20° and a cylinder with a fineness ratio of 5. Longitudinal flow over bodies has been studied numerically based on the Euler equation at a Mach number of incident flow equal to 4.03 and a zero angle of attack. The effect has been shown of the distance between the axes of models on the flow structure and disturbed and total aerodynamic characteristics of bodies. Calculated results have been compared with data of the physical experiment. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 81–90, July–August, 2006.     

Nonstationary processes on freshly exposed metal surfaces in various electrolytes

Summary Studies have been made on the nonstationary electrochemical processes at an NFS-auxiliary electrode-solution phase boundary. The maximum shift in the electrode potential and in the current density on interaction with the solution may be largely determined by the electrolyte type and pH. Comparison of measurements and calculations shows that the current density in a galvanic pair when NFS is formed exceeds that in the oxidation of iron alone. It is suggested that at the start of interaction, hydroxyl ions are discharged at a high rate with the formation of oxygen, whose specific contribution to the overall anodic current density is much greater than the current density due to the entry of the iron into solution. The data provide a new interpretation of the corrosion cracking mechanisms for metals in various electrolytes.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 25, No. 3, pp. 38–43, May–June, 1989.     

Stress singularities in bimaterial bodies of revolution

An eigenfunction expansion solution is first developed for determining the stress singularities of bimaterial bodies of revolution by directly solving the equilibrium equations of three-dimensional elasticity in terms of displacement functions. The characteristic equations are explicitly given for determining the stress singularities in the vicinity of the interface corner of two intersecting bodies of revolution having a sharp corner with free boundary conditions along the corner. The characteristic equations are found to be equivalent to a combination of the characteristic equations for plane elasticity problems and St. Venant torsion problems. The strength of stress singularities varying with the interface angles is also investigated. The first known asymptotic solutions for the displacement and stress fields are also explicitly shown for some interface angles. The present results will be useful not only for understanding the singularity behaviors of stresses in the vicinity of a revolution interface corner, but also for developing accurate numerical solutions with fast convergence for stress or vibration analysis of a body of revolution having an interface corner.     

Cyclic thermal creep model for the bodies of revolution

The new method of solving thermal creep problems, accounting for cyclic variations of external force and thermal fields was put forward. Asymptotic expansions and period averagings were used to derive the systems of basic and auxiliary equations. The equation of state for cyclic thermal creep was proposed and validated. Numerical simulation of the creep of cylinders under cyclic temperature variations was carried out.     

Propagation of waves in the interior of a thermoelastic dielectric half-space

This paper presents a plane Lamb problem for a semi-infinite thermoelastic dielectric body. The loading acting on the boundary is separated into two systems: the first is associated with the displacement field $\text{u}\text{?}\text{= (u}{}_1\text{, u}{}_2\text{, 0)}$, the polarization field, $\text{P}\text{?}\text{= (P}{}_1\text{, P}{}_2\text{, 0)}$, the electric potential field, φ, and the temperature field, θ; the second system is related to the components $\text{u}{}_3$ and $\text{P}{}_3$ only. A general solution for these systems is derived. The last section of the paper is devoted to 1-dimensional problems and the results therefrom are used to obtain a closed-form solution for the case in which the surface energy is assumed to vary harmonically and the boundary conditions are homogeneous.     

Angular coefficients in systems of bodies of revolution

The apparatus of differential geometry is used to calculate angular coefficients. Examples are given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 4, pp. 640–645, April, 1986.     

Nonstationary contact problem of thermoelasticity for bodies heated to different temperatures

The solution of a nonstationary contact problem of thermoelasticity for bodies heated to different temperatures is obtained by using the Laplace-Hankel integral transformation. The expression for contact pressure is deduced in the form of an explicit dependence on two unknown functions: the distribution of heat flow and the radius of the contact zone. An algorithm of simplified solution of the contact problem is proposed.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 3, pp. 51–61, May–June, 2004.     

Focusing of Rayleigh waves: simulation and experiments

A linear array of surface wave transducers has been developed to generate focused surface wave motion. A novel theoretical approach, whereby time-harmonic surface wave motion is represented by a carrier wave that satisfies a reduced wave equation on the surface of the body and supports the subsurface motion, is used to model the beam generated by a single element of the array. Comparison of theoretical and experimental results show that, for a single element, the opening angle of the beam is about 20 degrees and its cross-section can be represented by a Gaussian distribution of the normal displacements. For an eight-element array, the focused beam is subsequently obtained by superposition considerations. For the focused beam comparisons of theoretical and experimental results, in which the latter have been obtained by the use of a laser interferometer, show excellent agreement both for the normal displacements along a radial line and across the width of the beam. The array can be used for self-focusing of surface waves on a surface defect.     

Propagation of rayleigh waves in transversely isotropic generalized thermoelastic diffusion

This paper is devoted to the study of propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space that is subjected to stress-free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized theory of thermoelastic diffusion. The Lord and Shulman theory, where thermal and thermomechanical relaxation as well as diffusion relaxation are governed by two different time constants, is selected. Secular equations for surface wave propagation in the considered media are derived. The amplitudes of surface displacements, temperature change, and concentration are computed. The paths of the surface particles are determined. Transverse isotropy and diffusion effects on the phase velocity, group velocity, and attenuation coefficient are presented graphically.     

Propagation of harmonic thermoelastic waves in media with thermal memory

We present an analysis of the frequency dependence of phase velocities and damping coefficients of harmonic thermoelastic waves in media with thermal memory.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 4, pp. 655–662, April, 1988.