Propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder imbedded in a finitely prestrained infinite elastic body

Within the framework of a piecewise homogeneous body model and with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), the propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder (fiber) imbedded in a finitely prestrained infinite elastic body (matrix) is investigated. It is assumed that the fiber and matrix materials have the same density and are in compressible. The stress-strain relations for them are given through the Treloar potential. Numerical results regarding the influence of initial strains in the fiber and matrix on wave dispersion are presented and discussed. These results are obtained for the following cases: the fiber and matrix are both without initial strains; only the fiber is prestretched; only the matrix is prestretched; the fiber and matrix are both prestretched simultaneously; the fiber and matrix are both precompressed simultaneously. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 665–684, September–October, 2008.     

Surface acoustic waves in the testing of layered media. The waves’ sensitivity to variations in the properties of the individual layers

Research on the use of surface acoustic waves for the nondestructive testing of layered media is reviewed. A model to describe horizontally polarized surface acoustic waves in layered anisotropic (monoclinic) media is constructed. A modified transfer-matrix method is developed to obtain a solution. Non-canonical type waves with horizontal transverse polarization are investigated. Dispersion curves are constructed for a multilayer composite in contact with an anisotropic half-space. It is shown that the variation of the physical characteristics and the geometry of any of the internal layers leads to a variation in the dispersion curves. This opens up the possibility of using dispersion analysis for the nondestructive testing of the properties of the individual layers.     

Stability of smooth solitary waves for the generalized Korteweg–de-Vries equation with combined dispersion

The problem of orbital stability of smooth solitary waves in the generalized Korteweg–de-Vries equation with combined dispersion is considered. The results show that the smooth solitary waves are stable for any speed of wave propagation.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Modeling of Ultrasonic Waves in Fractured Rails with an Explicit Approach

Ultrasonic wave propagation in steel rails with explicit identification of flaws is numerically simulated. The problem is to detect a vertical crack in a railhead by applying ultrasonic nondestructive testing techniques. The propagation of elastic waves in the rail profile is simulated for various sizes and positions of the crack. It is shown that the finite-difference grid-characteristic method in the time domain and full-wave simulation can be used to analyze the effectiveness of rail flaw detection by applying ultrasonic nondestructive testing techniques. Full-wave simulation is also used to demonstrate the failure of the widely used echo-mirror method to detect flaws of certain types. It is shown that techniques for practical application of the ultrasonic delta method can be developed using full-wave supercomputer simulation. The study demonstrates a promising potential of geophysical methods as adapted to the analysis of ultrasonic nondestructive testing results.

     

Dispersion of torsional waves in initially stressed multilayered circular cylinders

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the propagation of torsional waves in prestressed multilayered circular cylinders is investigated. The elasticity relations for cylinder components are given through the Murnaghan potential. The influence of variations in the geometric and mechanical parameters of the cylinders on the dispersion curves is analyzed.     

Normal waves in orthotropic plates and prismatic bodies with thin face coatings

We construct and study the dispersion equations that describe the spectra of normal waves with various kinds of wave motion symmetry in a cross section of the waveguides. We compute the dispersion curve diagrams of symmetric waves for several directions of propagation in the plane of a plate and for the axial direction of a prismatic body of monocrystal Rochelle salt. Four figures. Bibliography: 4 titles Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 90–97.     

Bending normal waves in a crystal layer surrounded by a liquid

We obtain the dispersion relations that describe the spectrum of the “effluent” harmonic antisymmetric normal waves for an arbitrary direction in the plane of an orthotropic layer surrounded by a viscous or ideally compressible fluid. We present the results of computation of the lower branches of the dispersion spectrum for elastically equivalent directions of propagation in a layer of monocrystal Seignette salt in water. Four figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 123–131.     

Propagation of internal waves in a three-layer liquid

The propagation o f internal harmonic waves in a three-layer liquid is examined in a linear approximation for arbitrary wave numbers. A travelling wave sohaion is obtained and a dispersion equation is derived. The roots of the dispersion equation and the dependence of the solution on the ratio of the densities of the liquids are examined in detail. The phase and group velocities are plotted as functions of wavelength and graphs of the various wave modes are presented. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 170–174, 1999.     

Application of the ultrasonic method for the control of thermosetting polymer materials

Based on the theory of solid matter deformation and taking into consideration the specificity of propagation of ultrasonic waves in polymers, the acoustic nondestructive method has been chosen for controlling radiation-cured thermosetting polymer materials, which allows us to obtain certain information about the structure and useful characteristics of these materials. The correlation relationships of propagation velocities for flexural ultrasonic waves initiated in the material at a frequency of 60 kHz by piezotransducers-concentrators with exponential waveguides and point contact have been established. This permits us to determine the dose of ionizing radiation absorbed by the material, the degree of molecular orientation or degree of stretching, the content of fillers in the material, as well as to evaluate the thermosetting forces determined by thermorelaxation stresses under isometric conditions.Chemistry Department, University of Latvia, LV-1001. Institute of Polymer Materials, Riga Technical University, Riga, Latvia, LV-1048. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 394–407, May–June, 1997.     

On Periodic Wave Solutions to (1+1)-Dimensional Nonlinear Physical Models Using the Sine-Cosine Method

We investigate two interesting (1+1)-dimensional nonlinear partial differential evolution equations (NLPDEEs), namely the nonlinear dispersion equation with compact structures and the generalized Camassa–Holm (CH) equation describing the propagation of unidirectional shallow water waves on a flat bottom, and arising in the study of a certain non-Newtonian fluid. Using an interesting technique known as the sine-cosine method for investigating travelling wave solutions to NLPDEEs, we construct many new families of wave solutions to the previous NLPDEEs, amongst which the periodic waves, enriching the wide class of solutions to the above equations.     

The propagation of elastic waves in composite materials reinforced with piezoelectric fibres

The propagation of longitudinal elastic waves in composite materials, consisting of a polymer matrix reinforced by continuous fibres in one direction, is considered. The reinforcing fibres have piezoelectric properties and have a thin current-conducting coating (“shunted fibres”). The scattering of electric energy in such materials leads to dispersion of the velocity of the elastic waves and to their attenuation. The effective-field method is used to determine the macroscopic electroelastic constants of such composites. These constants enable one to obtain, in explicit form, the frequency dependence of the real and imaginary parts of the wave number of a longitudinal wave, propagating along the reinforcement direction, and also their dependenc on the physical and geometrical characteristics of the components.     

Comparison of methods for computing interference elastic waves in thin-layered media. 2

The paper is an immediate continuation of the paper where the solution of the problem on the propagation of low-frequency waves in thin-layered media by the dispersion equation method was considered in detail. In the present article, the solution of a similar problem is given for an elastic layer and a half-space, which are in rigid contact, by the method of superposition of complex plane waves. Bibliography: 17 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 217–232.     

Behavior of concrete cylinders confined by carbon composite 2. Prediction of strength

The mechanical behavior of round concrete cylinders confined by a carbon-epoxy composite wrapping is analyzed concerning the increased concrete compression strength due the wrapping. It is shown that the loading trajectories in the normalized stress space fit into a single master curve for all the concrete batches and jacket thicknesses investigated. The loading paths ended at failure of the composite wrapping from the increased internal lateral pressure. The strength of the composite was determined by split-disc tests of composite rings, but the strength of composite jackets realized on concrete specimens did not reach the strength of the rings. Therefore, a coefficient of composite strength reduction was introduced. A simple formula for predicting the strength of confined concrete is derived, and a comparison with fib (fédération internationale du béton) recommendations for strength predictions is given. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 165–178, April–May, 2006.     

Dissipative Boundary Conditions for Finite-Difference Problems in Elasticity Theory

Dissipative differential-difference boundary conditions for elasticity equations are derived and investigated. These conditions completely eliminate the longitudinal and transverse waves reflected from the boundary in case of normal incidence and substantially reduce the reflected waves in a wide range of other incidence angles. The dissipative boundary conditions reduce computer resource requirements for simulation of seismic wave propagation in unbounded regions. Grid analogues of the dissipative boundary conditions are constructed for a two-layer finite-difference scheme. Comparative results are reported for the solution of two-dimensional seismic problems using these boundary conditions for various incidence angles. __________ Translated from Prikladnaya Matematika i Informatika, No. 18, pp. 83–92, 2004.     

Some new solutions of the problems of wave propagation in a two-layer fluid

We present new analytic solutions of the problem of wave propagation in a continuously stratified fluid in the Boussinesq approximation. We study the propagation of internal waves in an ideal fluid in systems of homogeneous-layer/continuously stratified layer and homogeneous-layer/continuously stratified half-space type. We obtain the dispersion equations and study several limiting cases. Bibliography: 2 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, Vol. 27, 1997, pp. 132–137.     

Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation

Nonstationary solutions of the Cauchy problem are found for a model equation that includes complicated nonlinearity, dispersion, and dissipation terms and can describe the propagation of nonlinear longitudinal waves in rods. Earlier, within this model, complex behavior of traveling waves has been revealed; it can be regarded as discontinuity structures in solutions of the same equation that ignores dissipation and dispersion. As a result, for standard self-similar problems whose solutions are constructed from a sequence of Riemann waves and shock waves with stationary structure, these solutions become multivalued. The interaction of counterpropagating (or copropagating) nonlinear waves is studied in the case when the corresponding self-similar problems on the collision of discontinuities have a nonunique solution. In addition, situations are considered when the interaction of waves for large times gives rise to asymptotics containing discontinuities with nonstationary periodic oscillating structure.     

General Theory of Acoustic Wave Propagation in Liquids and Gases

We study the propagation of small-amplitude acoustic waves in liquids and gases and use the hydrodynamic equations to obtain an exact dispersion equation. This equation in dimensionless variables contains only two material constants p and q. We solve the dispersion equation, obtaining an exact solution that holds for all values of the parameters and all frequencies up to hypersonic, and thus analytically establish exactly how the speed of sound c, the wave vector k, and the damping factor x depend on the frequency ω and the dimensionless material constants p and q. Studying the behavior of the solution in the sonic and ultrasonic frequency bands for ω < 10⁷ sec^-1 results in an expression for the damping factor, which differs from the Kirchhoff formula. The speed of sound c and the wave vector k are shown to have finite nonzero values for all hypersonic frequencies. At the same time, there exists a certain maximum frequency value, ω_max ≈ 10¹¹-10¹² sec^-1, at which the damping factor x is zero. This frequency determines the boundary of the applicability domain for the hydrodynamic equations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 340–352, February, 2006.