Dispersion and attenuation of torsional wave in a viscoelastic layer bonded between a layer and a half-space of dry sandy media

Propagation of a torsional wave in a doubly-layered half-space structure of an initially stressed heterogeneous viscoelastic layer sandwiched between a layer and a half-space of heterogeneous dry sandy media is studied. A closed form complex expression for the velocity profile is obtained under effective boundary conditions. The real part of the complex expression provides a dispersion equation, and the imaginary part yields a damping equation. The derived dispersion and damped equations are in well agreement with the classical Love wave condition. In addition, to study the effect of the dissipation factor, the attenuation coefficient, the sandy parameters, the initial stress, the heterogeneity parameters, and the thickness ratio parameter, some noteworthy contemplations are made by numerical calculations and graphical visuals. The results of this paper may present a deeper insight into the behaviour of propagation phenomena in heterogeneous viscoelastic and heterogeneous dry sandy materials that can provide a theoretical guide for the design and optimization in the field of earthquake engineering. The study also reveals that the presence of a damping part due to viscoelasticity affects the torsional wave propagation significantly.     

Self-switching of a transverse plane wave propagating through a two-component elastic composite

The paper discusses the results of theoretical and numerical analysis of the interaction of nonlinear elastic plane harmonic waves in a composite material whose nonlinear properties are described by modeling it with a two-phase mixture. The interaction of two transverse vertically polarized harmonic waves is studied using the method of slowly varying amplitudes. The truncated and evolutionary equations as well as the Manley-Rowe relations are derived. The mechanism of energy pumping from a strong pumping wave with frequency ω to a weak signal wave with frequency 3ω is analyzed. The switching mechanism for hypersonic waves in a nonlinear elastic composite is similar to the switching mechanism observed in transistors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 35–46, July 2007.     

Rayleigh-type wave propagation through liquid layer over corrugated substrate

The propagation of the Rayleigh-type wave in a fluid layer overlying a corrugated substrate is studied. The corrugated substrate is considered as a fluid saturated poroelastic substrate and a quadratically heterogeneous isotropic elastic substrate in Case I and Case II, respectively. Closed form expressions of dispersion relation for Case I and Case II are obtained. The influence of corrugation, porosity, and heterogeneity on the phase velocity of Rayleigh-type wave, for both cases, is highlighted and demonstrated through numerical computation and graphical discussion. Neglecting corrugation at the common interface, expressions of phase velocity of the Rayleigh-type wave for both cases are derived in a closed form as a special case of the problem. Comparison between the presence and the absence of both heterogeneity and poroelasticity in the substrate of the composite structure is a key in the present study.     

Study of the attenuation of a detonation wave with a two-front structure by the boundary (shock) layer method

The possibility that a plane overcompressed detonation wave may undergo a transition to the Chapman-Jouguet mode during its attenuation is considered on the basis of the two-front model, allowing for the change in flow parameters in the interval between the fronts. G. G. Chernyi's approximate method of boundary (shock) layer is used in order to describe the flow of the gas in this interval. The use of this method is justified by the fact that the velocity of propagation of the detonation wave is extremely great (order of several km/sec), and the gas between the compression jump and the combustion front is strongly compressed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp. 59–65, May–June, 1971.     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

Nonlinear development of a wave in a boundary layer

In recent years definite progress has been achieved in the construction of theoretical models of nonlinear wave processes which lead to a transition from laminar to turbulent flow [1, 2]. At the same time, there is a shortage of actual experimental material, especially for flows in a boundary layer. Fairly thorough experimental studies have been carried out only on the initial stage of the development of disturbances in a boundary layer, which is satisfactorily describable by the linear theory of hydrodynamic stability. In evaluating the theoretical models of subsequent stages of the transition, investigators have been forced to turn chiefly to much earlier experiments carried out by the United States National Bureau of Standards [3, 4], in which the main attention was concentrated on the three-dimensional structure of the transition region. The present investigation was undertaken for the purpose of obtaining detailed data on the structure of the flow in the transition region when there is disturbance in the laminar boundary layer of a two-dimensional wave. In order to make the two-dimensional nonlinear effects stand out more clearly, the amplitude of the wave was specified to be fairly large from the very outset. In contrast to earlier investigations, the main attention was centered on the study of the spectral composition of the disturbance field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–58, May–June, 1977.     

Propagation and attenuation of waves generated in a layer by a plane source

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 35–41, September–October, 1990.     

Nondispersive wave propagation in a layered composite

It is found that it is possible to propagate a horizontally polarized (SH) wave without dispersion through an elastic, periodically-layered composite. The nondispersive property of the wave is due to the fact that at each interface the angle of incidence is such that the wave is totally transmitted without reflection. In optics such an angle is referred to as the Brewster angle. It is determined that this particular case is contained as a special solution of the general dispersion equation for SH waves, which has not been noticed before.     

Elastic field of a composite cylinder with a spatially varying dynamic eigenstrain

The analytical solutions of displacements and stresses for an eigenstrain problem in a composite bi-layered coaxial cylinder are presented in this article. The inner cylinder is assumed to undergo a dynamic, spatially varying eigenstrain. The spatial distribution of the eigenstrian is taken to be a quadratic polynomial with arbitrary coefficients along the radial direction. Furthermore, the eigenstrain is assumed to be harmonically time-dependent. Elasticity equations are constructed to directly solve the problem. The effect of spatial distribution, as well as the angular frequency of the eigenstrain on the elastic response of the composite cylinder has been illustrated graphically.     

Nonlinear wave processes in a hypersonic shock layer

Nonlinear disturbance development in a hypersonic flat-plate shock layer (M_∞ = 21, Re _L = 1.44×10⁵) exposed to external-flow slow-mode acoustic perturbations at one or several frequencies is studied on the basis of the numerical solution of the Navier-Stokes equations. The mean flow distortion by disturbances and the nonlinear self-interaction between spectral modes is investigated by varying the initial amplitudes of the acoustic waves introduced. The appearance of combination frequencies, both summarized and subtracted, and their interaction with each other is shown to exist.     

Resonant interaction of wave packets in a boundary layer

The space-time evolution of resonance-coupled triads of wave packets in a Blasius boundary layer is studied within the framework of weakly nonlinear stability theory. The amplitude behavior of the packet envelopes is determined in relation to their initial shape, the carrier frequency and the region of propagation. As in the case of triads with a discrete spectrum, interaction leads to parametric pumping of the low-frequency fluctuations and explosive nonlinear growth of the packet maxima. The space-time evolution characteristics are expressed in the deformation of the shape and the spectra of the disturbance. Parts of the envelopes are amplified, depending on the local values of the parameters. This leads to sharp discrimination of the peaks and the equalization of their propagation velocities. These effects make it possible to explain the broadening of the spectrum, the stable distribution of the visualization pattern, and the appearance of irregularities in the oscillograms observed in the S transition. In order to analyze the nonlinear evolution of a disturbance initiated by an instantaneous point source, the interaction of a two-dimensional wave train with variable carrier frequency and pairs of three-dimensional low-frequency packets is examined. (The train frequency corresponds to the local maximum of the linear growth rate with respect to R.) The possibility of the progressive parametric excitation of fluctuations over the entire band of frequency parameters is established. This may explain the acceleration of the transition process in the presence of an impulsive disturbance of the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 67–71, November–December, 1988.The authors are grateful to I. I. Maslennikov for useful discussions.     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

Correlation of elastic wave attenuation and scattering with volumetric grain size distribution for polycrystals of statistically equiaxed grains

This study establishes an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains by extending a prior study (Sha, JASA, 2018). This relation is further validated by applying it to available TPCF and volumetric grain size distribution in the literature. Based on this relation, analytical attenuation coefficients for longitudinal and transverse waves, accounting for volumetric grain size distribution, are derived under Born approximation for macroscopically isotropic polycrystals of equiaxed triclinic grains. These attenuation models are applicable for whole frequency range except geometric region. Moreover, scattering coefficients for a polycrystal of equiaxed triclinic grains with a volumetric grain size distribution are obtained. Finally, the analytical attenuation model for the longitudinal wave is verified by comparison with existing 3D finite element simulation results in the literature. This theoretic study has practical applications to the inverse determination of volumetric grain size distribution from ultrasonic measurements.     

Oscillations of a shock wave induced by boundary layer separation

The causes of the oscillation of the separation-induced shock formed in supersonic flow over a step are investigated on the basis of measurements of the spatial correlations of the boundary pressure fluctuations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 168–170, July–August, 1990.     

Resonance properties of two-dimensional wave disturbances in a boundary layer

The nonlinear development of disturbances of the traveling wave type in the boundary layer on a flat plate is examined. The investigation is restricted to two-dimensional disturbances periodic with respect to the longitudinal space coordinate and evolving in time. Attention is concentrated on the interactions of two waves of finite amplitude with multiple wave numbers. The problem is solved by numerically integrating the Navier-Stokes equations for an incompressible fluid. The pseudospectral method used in the calculations is an extension to the multidimensional case of a method previously developed by the authors [1, 2] in connection with the study of nonlinear wave processes in one-dimensional systems. Its use makes it possible to obtain reliable results even at very large amplitudes of the velocity perturbations (up to 20% of the free-stream velocity). The time dependence of the amplitudes of the disturbances and their phase velocities is determined. It is shown that for a fairly large amplitude of the harmonic and a particular choice of wave number and Reynolds number the interacting waves are synchronized. In this case the amplitude of the subharmonic grows strongly and quickly reaches a value comparable with that for the harmonic. As distinct from the resonance effects reported in [3, 4], which are typical only of the three-dimensional problem, the effect described is essentially two-dimensional.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 37–44, March–April, 1990.