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It has been shown that account of elastic nonlinearity during the propagation of an acoustic wave in a solid lead to the appearance of a quadratic nonlinearity, which in its turn leads to the possibility of generating a wave of double frequency, the interaction of harmonics is asymmetric. The conditions under which nonlinear stationary waves are formed are considered. A phase portrait is constructed, and the dependence of the wavenumber of a nonlinear wave on its amplitude is estimated.

In this paper, we experimentally determine the drag coefficient when conical and cylindrical impactors penetrate into sandy soil. In the experiments, the half-opening angle of the conical tip of the penetrator (indenter) varied from 10° to 90°. The velocity of indenter movement varied in the range of 0.2–2.0 km/s. The average values of the drag coefficient are obtained for conical bodies during quasi-stationary supersonic motion in sandy soil with an average moisture content of 7–12% and for indenters with a flat front end in sandy soil with a moisture content of 0–16%. A significant dependence of the drag coefficient of thin cones (β < 25°) on the movement velocity and the absence of such a dependence (taking into account the experimental error) for obtuse cones and an indenter with a flat end were shown.

The propagation of plane longitudinal waves in an infinite medium with point defects has been investigated. The medium is assumed to be placed in a nonstationary nonuniform temperature field. A self-consistent problem considering both the influence of the acoustic wave on the generation and displacement of point defects and, conversely, the influence of point defects on the propagation of the acoustic wave has been considered. It has been shown that in the absence of heat diffusion, the corresponding set of equations reduces to a nonlinear evolutionary equation in particle displacements in the medium. This equation can be viewed as a formal generalization of the Korteweg–de Vries–Burgers equation. Using the finite difference method, an exact solution to the evolutionary equation in the form of a monotonically decreasing stationary shock wave has been found. It has been noted that defect-induced dissipation dominates over dispersion due to defect migration.

In this paper, a mathematical model is formulated (in linear and nonlinear formulations) and investigated, which makes it possible to describe the propagation of flexural waves in a beam taking into account the damage of its material. An approach is proposed that determines new dependences of the flexural waves parameters on the material damage degree. This approach makes it possible to formulate a self-consistent problem that includes the equations of material dynamics and the conditions for its destruction. In the framework of a geometrically nonlinear model of a damaged rod, the problem of the intense bending waves formation of a stationary profile is considered. It is shown that such essentially non-sinusoidal waves can be either periodic or solitary (localized in space). The dependencies connecting the parameters of the waves (amplitude, width, wavelength) with the damage to the material are determined. It is shown that the periodic waves amplitude and the solitary waves amplitude increase with increasing material damage parameter, in turn, the periodic waves length and the solitary waves width decrease with increasing this parameter.

Calculating results on the nature of aerodynamic interaction of cube objects are presented for a velocity range from 2 up to 10 Mach numbers. The objects were arbitrary oriented relatively to moving flow. The examined objects have a character size 8 mm. The method of numerical solution of the complete Navier-Stokes equations averaged according to Reynolds and supplemented by a simple turbulence model has been selected for simulations. The complete picture of the flow past a single cube was built taking into account its orientation relative to the flow direction. Three-dimensional calculation of the process of exterior flow around considered objects by a supersonic gas flow was conducted taking into account appropriate boundary conditions on the surfaces of objects and on the walls of a calculation domain. The equation of state of the perfect gas was used for air. The aerodynamic forces and moments acting on streamlined surfaces of objects and also all parameters of the gas flowing in a calculation volume - pressure, density, temperature and velocity fields were determined as a result of solution. The complete calculation was divided into several stages, in the end of which the automatic analysis of an obtained solution was made and the coarse mesh refinement based on this analysis was conducted in high-gradient areas of flow parameters. The complete number of counting cells n in a concrete calculation, as a rule, did not exceed 2.5Ч106. The precision of obtained results was estimated by the character of solution convergence on each of considered calculation stages. The symmetry conditions were used for the decrease of a calculation domain. During calculation such aerodynamic characteristics of each object as the drag coefficient was determined. The value of drag coefficient in dependence of velocity plays important role in splinter ballistics. For comparison the results of supersonic experiments for cube splinters arbitrary oriented relatively to moving flow are presented. Visualization of the flow about the cube samples was performed using shadow technique. The character of ablation due to aerothermomechanical destruction is shown with pulsed roengraphy. Experiments have been carried out in aeroballistic range using powder ballistic launchers. In the presented X-ray image the shape of the steel cube undergoing hypersonic flow is shown.

The applicability of the shadow background method for registering non-spherical shock waves is demonstrated. In contrast with measuring using pressure indicators, the shadow background method makes it possible to obtain 2D pictures of shock wave propagation. The method requires the presence of a simplest background (grass, sand, wood), a camcorder and a computer. A shock wave is caused by an explosive charge of a cylindrical form. To visualize the shock wave, the illumination produced by the explosion of the charge is registered. A series of successive pictures of the explosion process is obtained. Based on their analysis, curves of excessive pressure along the shock wave front as a function of time are constructed. The visualization shows inhomogeneous distribution of the shock wave. The inhomogeneity of the excessive pressure along the shock wave front decreases as the wave propagates on. It is demonstrated that, based on the results of visualization of the shock wave, it is possible to determine the explosion center in the registration plane. The authors believe that the use of multi-aspect video-registration will make it possible to obtain 3D pictures of shock wave propagation and to determine explosion center coordinates in space. Keywords: shadow background method, explosion, shock wave, rapid video-registration.

On the base of assumption that the rotational movements of the chain of the crust blocks and the corresponding rotational waves characterizing the redistribution of tectonic stresses are described by the sine-Gordon equation with dissipation, the dispersion properties of this equation are analyzed. It is shown that the dispersion is manifested in the low-frequency range at high values of the dissipation factor. The presence of anomalous dispersion has been revealed for all values of the dissipation factor. Influence of this factor on dispersion is investigated. Some features of propagation of a stationary shock wave in a geomedium are studied. It has been found that the shock wave front width is directly proportional to the nonlinear wave velocity and to the dissipation factor of the medium, but it is inversely proportional to the nonlinearity coefficient.

Propagation of a plane longitudinal acoustic wave in a solid with dislocations is theoretically studied. The effect of dislocations on the phase velocity dispersion and the character and degree of wave damping is analyzed. The following results are obtained. The phase velocity exhibits infinite growth at zero frequency and asymptotically approaches the tabulated value for the longitudinal wave velocity in solids as the frequency tends to infinity. The frequency dependence of the wave damping coefficient has a peak whose position depends on the characteristics of the solid. The results are compared with experimental data for the dislocation relaxation process in lead and are found to be in good agreement with these. The influence of the dislocation structure on the character of the dependencies obtained for wave damping and phase velocity dispersion is analyzed. The results are compared with experimental data for the dislocation damping during plastic deformation and cycling loading of polycrystalline copper and aluminum. We derive the dynamic equations of solid media with dislocations containing geometrical and physical nonlinearity. The evolution of nonlinear acoustical waves under the influence of a dislocation field is studied. The development of modulation instability quasiharmonic longitudinal waves is shown to be possible.

The problem of longitudinal wave propagation in a rod made from an auxetic material is considered. It is shown that a negative Poisson’s ratio leads to a qualitatively different (anomalous) dispersion behavior of linear waves. Accounting for geometric and physical elastic nonlinearities leads to the possibility of generating in a rod of stationary strain waves of a substantially non-sinusoidal profile—solitons and their periodic analogues. By means of numerical simulation it is shown that qualitatively different scenarios of interaction of solitons depend on the relative collision velocity.

A self-consistent dynamic problem is posed for a system including a one-dimensional flexible guide (a string), elastic-inertial foundation (an array of oscillators), and moving oscillating load. The effect of the foundation parameters on the dispersion characteristics (frequency, phase velocity, and group velocity as functions of the wavenumber) of transverse waves propagating along the string has been analyzed. It has been shown that taking into account the foundation inertia leads to the presence of two critical (cutoff) frequencies. Regularities of wave generation by a source moving along the string have been analyzed.

A possible way of study of single waves in solids is discussed. The soliton is one of these waves without shape and parameters varying. Soliton deformation parameters are connected with the elastic moduli of the third order that allows defining values of these moduli by means of the measured solitondeformation parameters in various type waveguides made of the same material. The conditions under which a soliton can exist in a rod are analytically determined. For simultaneous excitation of loading in several wave guides two new energetic photosensitive structures (the mixtures are given) initiated by means of short light impulses of noncoherent light sources are proposed. Conditions of excitation of the waves on the basis of multipoint optical initiation loading impulses are described. As a technique for registration the shadowgraph visualization is proposed. It is discussed, how the problem connected to the use of energetic initiation structures consisting in the power background illumination can be solved. The shadow scheme with the use of a tiny dot explosive light source (Tbr ~41 kK) allows to carry out modelling experiments on research of slabbing actions, jet formations, fluffings, hydrodynamic instability during shock-wave loading of investigated samples, which makes it attractive for determination of parameters in equations-of-state for investigated materials, creation of numerical models and their validation. Some examples showing basic possibility of application of the declared techniques are included.

The work is devoted to the study of the stability of mechanical systems with moving loads. We consider lumped objects that move uniformly along the distributed elastic systems. For example, sliding train supports vibrating, excited in the rails elastic waves, which can lead to instability.

A one-dimensional model of a granular medium with internal stress is considered that represents a chain consisting of elastically interacting ellipsoidal-shaped particles, which possesses translational and rotational degrees of freedom. By means of a long-wavelength approximation, nonlinear differential equations have been derived that describe the propagation of longitudinal, transverse and rotational waves in such a medium. Analytical dependencies of the velocities of elastic waves and the nonlinearity coefficients on the sizes of particles and the parameters of interactions between them have been found. If longitudinal waves are not excited in the medium and in the field of low frequencies, when the rotational degree of freedom of particles can be neglected, the obtained three-mode system reduces to one equation for the transverse mode. On the base of this equation containing cubic nonlinearity, numerical investigations of counter and passing interactions of strongly nonlinear soliton-like subsonic and supersonic waves have been performed. In particular, effects of splitting of supersonic solitary waves are demonstrated.

We consider an elastic plate made of conductive material in an external magnetic field. It is shown that the distribution of intense waves in such a system can be described by nonlinear evolution equations, combining the well-known Khokhlov–Zabolotskaya–Kuznetsov and Kodomtsev–Petviashvili model equations. The features of the propagation of two-dimensional nonlinear magnetoelastic waves are analytically and numerically analyzed.