Pipes conveying fluid are considered as a fundamental dynamical problem in the field of fluid- structure interaction. They are widely used in the petroleum industry, in nuclear engineering, aviation and aerospace, in nanostructures. This article investigates the effect of temperature load on the dynamic stability of a straight pipe conveying pulsatile flow. The fluid velocity is a harmonic function of time. The Galerkin method is applied for the solution of the differential equation of the transverse vibrations of the pipe. The differential equation is reduced to a first-order differential equation system. The system of differential equations is transformed and rewritten in a matrix form. The harmonic function of the fluid velocity allows the Floquet theory to be applied in order to investigate the dynamic stability of the system. The static scheme of the investigated pipe is a beam with restricted horizontal and vertical displacements at both of its ends. A numerical solution for a straight pipe conveying fluid with specified geometric and physical characteristics has been carried out. The temperature load and the constant fluid rate are considered as parameters of the problem. The results show that the temperature load affects the vibrational characteristics of the pipe, as well as its critical velocity.

Forging processes are traditional methods of metalworking, their application is very extensive and allows the manufacture of metal products for various industries in a wide temperature range. The redistribution of the main acting forces during forming is a necessary condition for the transfer of traditional forging methods to high-tech methods of metal production. The main products of press-forging production are forgings such as pallets and plates. In the present work, the effect of shear forces on the stress-strain state is studied when the friction forces are redistributed on the contact surface and/or the nature of the metal flow changes during upsetting of wide strips. The analysis of the stress state was carried out by the method of slip lines compared with the existing method of settlement without shear. The field of slip lines and the hodograph of velocities for the draft of the strip with a shift are compiled. The stresses and intensity of the shear deformation were estimated by the analytical method. It was revealed that the upsetting of the strip between plane-parallel plates is accompanied by extremely uneven deformation over the section of the workpiece. The stress state is compared with traditional deformation and with superimposed shear deformation. The use of shears made it possible to realize predominantly compressive stresses, which make it possible to eliminate internal defects of the workpiece of foundry origin. The introduction of shear deformations contributes to the intensification of the plastic deformation process over the entire cross section of the strip, the stress values during draft with additional shear increase on average 4-6 times compared to normal draft. The increase in stress occurs due to the development of the intensity of shear deformation, reaching a value of 0.4 per compression.

When modeling liquid filtration in a porous medium, it is assumed that the filtration coefficient is constant, as a result of which the solution is simplified and reduced to a boundary value problem for the Laplace equation. In this paper, the almost periodic of Bohr analytical solutions of the plane problem of steady-state liquid filtration in an elastic – porous piecewise inhomogeneous domain are constructed using a generalized discrete Fourier transform . The domain is a strip consisting of several layers (strips) with different elastic and filtration parameters. Assuming that the filtration coefficient of an elastic-porous medium depends on the first invariant of the stress tensor, we consider it linearly dependent on the coordinate varying along the bandwidth. The filtration problem is reduced to solving a system of partial differential equations with specified boundary conditions on the upper and lower boundaries of the entire multilayer strip and conditions on the internal lines of the media interface, which in turn is reduced to solving the Cauchy problem for a system of Bessel ordinary differential equations. All solutions in this paper are obtained in the form of absolutely convergent Bohr-Fourier series, the coefficients of which are expressed in terms of given functions. Fluid filtration in a three-layer strip consisting of various light and sufficiently elastic-porous sedimentary and igneous rock layers is modeled. Graphs of the desired mechanical parameters are constructed. Their convergence to boundary conditions and conditions on the interface lines of media is shown. The paper also provides basic information concerning the properties of almost-periodic functions and the generalized discrete Fourier transform necessary for a more detailed understanding of the problem.

The object of study. The upper upward position of the pendulum subjected to vibration of the pendulum base is known to be stable for some parameters of the base vibration. The research is devoted to dynamics of the model of a two-link inverted pendulum in a general nonlinear formulation. The goal. The boundaries of the parameters of a given base vibration, under which the inverted mode is stable, are assumed to be known. The goal is to find the regions of the initial conditions of the problem, namely, the initial non-small angles of deviation of the pendulum links from the vertical that result in stable oscillation in the inverted position. We intend to reveal the impact of the rod compressibility on the oscillation mode, as well as the influence of the resonance on stability in the framework of more complex formulation of the problem which involves account for small elastic axial deformation in the rods. Methods. By applying the laws of dynamics to the moving elements of the structure, we derive the complete nonlinear system of equations of the pendulum motion in two formulations: (i) for a system with two and (ii) four degrees of freedom, respectively. The equations include the parameter of small base vibration amplitude, which makes it possible to apply the two-scale asymptotic expansion method. The method leads to a system of averaged equations of motion which is convenient for the benchmark study of parameters. Results. The modes and eigenfrequencies of small oscillations of the pendulum are found depending on the dimensionless parameter of the problem. In the nonlinear for-mulation, the maximum deviations of the pendulum links are calculated which ensure a stable solution to the problem for zero initial angular velocities. Depending on the initial phase of vibration of the base, the boundaries of absolute and partial zones of stability of vibrations are obtained. In the absolute zone, stable oscillations are realized for any value of the initial phase of the base vibration. In the partial region, stable oscillation occurs at least for one set of initial condition. The dynamics of the pendulum is compared with and without account for rod the compressibility. The results are presented in the graphs.

An approach to modeling dynamic processes in a semi-infinite composite plate of inhomogeneous piezoelectric and dielectric layers is proposed. When modeling the inhomogeneity of the layers, a two-component model with a functionally gradient change in properties was used, in which the physical parameters of the base material continu-ously change along the thickness up to the inclusion parameters. The material of the piezoelectric layer is a combination of PZT-based piezoceramics with a significant differ-ence in speed characteristics. The possibility of localizing the inhomogeneity both at the outer surface of the plate, and in the middle of the layer or at the interface has been im-plemented. The dielectric layer is made of SiO2, the inhomogeneity of the dielectric layer models the interpenetration of the piezoelectric and the dielectric in a narrow transition region near the interface. The elastic and dielectric moduli of the piezoelectric material located near the interface were considered as parameters of the inclusion material. The outer surfaces of the composite plate are stress-free and electrically short-circuited. The problem of the propagation of surface SH-waves in a composite structure of functionally gradient piezo- and dielectric layers initiated by the action of an infinitely distant source of harmonic oscillations is considered. The solution is constructed in the space of Fou-rier images by reducing to the solution of a system of ordinary differential equations with variable coefficients, which in turn is constructed using the Runge – Kutta – Merson method. The dispersion equation of the problem is presented, the analysis of which made it possible to investigate the influence of the nature, size of the transition region of materials and localization of structural inhomogeneity on the behavior of SAW phase velocities for a wide frequency range. The results obtained are given in dimensionless parameters and may be of particular interest in the development, design and optimization of new materials for micro- and nanoscale devices and devices based on SH SAW with high performance characteristics.

The dynamics of a Bernoulli – Euler beam lying on an elastic foundation is consid-ered. A generalized model of an elastic foundation is selected, which includes two inde-pendent bedding coefficients: the stiffness of the foundation for tensile-compression deformation and for shear deformation. Unlike the classical elastic foundation model (Winkler's model), the generalized model takes into account the distribution capacity of the soil, i.e. its property to settle not only under the loaded area, under the foundation, but also near it. The beam is considered to be infinite. Such idealization is permissible if optimal damping devices are located on its boundaries, that is, the parameters of the boundary fixation are such that the perturbations falling on it will not be reflected. This makes it possible to consider the beam model without taking into account the boundary conditions, and consider vibrations propagating along the beam as traveling bending waves. The influence of a two-constant elastic foundation on the parameters of a bending wave propagating in a beam is studied. It is shown that with an increase in the shear stiffness of the elastic base, waves with the same wavenumber (i.e., waves of the same length) will have a higher frequency, higher phase and group velocities. For the system under consideration, the energy transfer equation is written in divergent form. It is shown that the average rate of energy transfer is equal to the group velocity of the flexural wave. The equality of these velocities serves as an additional factor indicating the internal physical consistency of the model of bending vibrations of a beam lying on a general-ized elastic foundation.

This paper reports the results of a study on the structure and properties of elasto-meric nanocomposites based on polyurethane, which is of special interest due to its heterogeneous structure. So, the unfilled polyurethane also can be considered as a nanocomposite with complex mechanical behavior. Our study was performed on unfilled polyurethane and polyurethane filled with carbon particles of various morphologies: 1) few-layer graphene; 2) multi-walled carbon nanotubes; 3) diamond charge (detonation nanodiamonds). The content of filler in composites was 0.5 and 4 phr. Analysis of the mechanical behavior of the materials under consideration was car-ried out on the basis of the results of classical uniaxial tensile tests and cyclic experi-ments with increasing amplitude of deformation. The results obtained demonstrated that the incorporation of even a small filler amount in a polyurethane matrix leads to a signifi-cant change in the mechanical properties of the material. First of all, the stiffness of the material decreases in all cases. Secondly, the rupture (tensile failure) of the filled material significantly increases (almost in all cases) as compared to the unfilled polyurethane. The true stresses in some materials also increase at the time of sample’s rupture. A series of tearing tests were performed to gain a deep insight into the peculiarities of the failure mechanisms of materials. It was established that an increase in the macro-fracture of the unfilled material (until its rupture) is insignificant. In the materials rein-forced with nanofillers, the growth of macrofractures takes a longer time, and they prop-agate to a much greater extent. Numerical calculations were carried out to give an explanation for the reduction in the polyurethane stiffness and the macrofracture growth retardation when the filler is added to polyurethane. It was hypothesized that a soft interfacial layer is formed near the particle surface. Furthermore, the finite element model proposed here can be used to explain the growth of deformations at the moment of rupture for filled polyurethane sys-tems.