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The influence of the material properties of a pre-stressed cylinder containing a compressible inviscid fluid on the dispersion of axisymmetric quasi-Scholte waves is studied. It is supposed that the inhomogeneous pre-stresses in the cylinder are caused by the fluid pressure acting on the internal face surface of the cylinder before the wave propagation. The motion of the cylinder during wave propagation is described by the so-called three-dimensional linearized equations of the theory of elastic waves in bodies with initial stresses, and the flow of the fluid, by the linearized Euler equations. For solving the corresponding eigenvalue problem, the discrete–analytical solution method is employed and the related dispersion equation is solved numerically. The dispersion curves containing the first roots of the dispersion equation refer to quasi-Scholte waves, which play an important role in helping to understand the solid–fluid dynamic interaction. A study of the influence of the cylinder material properties on the character of these curves is the main novelty of the present paper. The numerical results are presented and discussed on. For this purpose, steel, aluminum, lucite, and soft rubber are selected as cylinder materials, and water is chosen as the fluid. It is established, in particular, according to the numerical results, that an increase in the shear wave velocity in the cylinder material causes an increase in the propagation velocity of quasi-Scholte waves. [ABSTRACT FROM AUTHOR]

Experimental tests of a seven-bolted connection with an asymmetric contact area between the joined elements are presented. The research is divided into two stages. In the first one, the connection is preloaded in a three-pass cycle. In the second stage, the connection is loaded with a monotonic alternating force applied at an angle of 30 degrees to the contact surface of the joined elements to generate compressive and shear forces in the connection. The tests are carried out with the use of the INSTRON 8850 testing machine. As a result, the courses of forces in the bolts measured with the use of resistance strain gauges and the relative displacements between the joined elements measured with an extensometer are shown. In the second part, the modeling of the connection in the convention of the finite element method is presented. The joined elements are modeled with the use of spatial finite elements, and the fasteners, as the hybrid elements made of deformable beams, rigid heads, and rigid nuts. The paper is completed with a comparison of the results obtained from the measurements and calculations, based on which the conclusions important from the point of view of the FEM analysis are drawn. [ABSTRACT FROM AUTHOR]

The paper provides information about the history of the Department of Mechanics, the scientific directions, and some research results of the institutes of the Department. Brief information about the heads of the Department since its foundation, founders and current heads of the institutes of the Department is presented. Information on the cooperation of the institutes of the Department with leading industrial enterprises and universities in Ukraine and abroad is provided. [ABSTRACT FROM AUTHOR]

The paper deals with the study of the influence of the inhomogeneous residual stresses caused by the "contact" of a cut on the dispersion of axisymmetric longitudinal waves in a two-layer hollow cylinder. According to the classification of Guz, this study is carried out using the second version of the small initial deformation of the linearized 3D theory of elastic waves in bodies with initial stresses. The discrete analytical method developed by the authors is used to solve the corresponding field equations. Numerical results illustrating the influence of residual stresses on the dispersion curves are presented and discussed. The magnitude of the residual stresses is estimated by the intersection (cutting) angle as a result of contacting, through which the residual stresses occur in the layers of the cylinder. [ABSTRACT FROM AUTHOR]

This paper presents a brief survey of the Series of Scientific Monographs "Stability and Control: Theory, Methods and Applications" published during 1995–2002 at the Gordon and Breach Science Publishers (UK) and the Taylor and Frances Publisher (USA). The Series comprises 22 volumes and is encyclopedic in the field of stability and control theories. Moreover, the history of appearance and realization of the idea of publishing the Series is outlined. [ABSTRACT FROM AUTHOR]

The results of experimental studies on the effect of randomly located circular holes of various number and diameters on the critical buckling force of longitudinally compressed cylindrical shells are presented in the form of curves of the critical buckling load versus the number, size, and total area of the random holes and the buckling patterns. The obtained data can be useful for predicting the residual load-bearing capacity of damaged shell structures. [ABSTRACT FROM AUTHOR]

A new type of combined honeycomb structure produced by optimally organizing the hexagons and square unit cells is proposed. The related equivalent elastic parameters are studied based on the strain energy equivalent theory. A numerical simulation method is used to verify the correctness of the equivalent mechanical model. A good agreement between the simulation values and theoretical solutions is observed. The study of mechanical properties of the combined honeycomb structure shows the great advantages in mechanical properties as compared with the traditional hexagonal honeycomb structure. With the same equivalent density, the in-plane equivalent elastic modulus of the new combined honeycomb is improved to 22%, the shear modulus enhanced to 95%. The external equivalent elastic modulus and shear modulus are improved to 33% and 29%, respectively. The carried out study provides a theoretical basis for the combined honeycomb structure's further research and also gives a new way to improve the current honeycomb sandwich. [ABSTRACT FROM AUTHOR]

The dynamics of three-layer cylindrical elements with an inhomogeneous filler rested on the Winkler elastic foundation under various boundary conditions is studied. The distances between ribs in the light filler are much larger than the dimensions of the ribs cross-sections. Because of this, the theory of independent static and kinematic hypotheses is applied to each layer. In accordance with the Hamilton-Ostrogradsky variational principle the motion equations of the three-layer cylindrical shells rested on the Winkler elastic foundation and natural boundary conditions are obtained using the models of Timoshenko's shell and rod theory. This made it possible to produce an adequate finite-element model for three-layer cylindrical shells of different materials and obtained numerical results of the nature of dynamic behavior of a three-layer structure on an elastic foundation by employing the finite element method. The influence of the physical-mechanical parameters of layers of cylindrical structures on natural frequencies, methods of fastening their ends, parameter of shells elastic foundation on their dynamics under axisymmetric internal impulsive loading is investigated. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]

The propagation of axisymmetric waves in a hollow homogeneous piezoceramic cylinder with different electrical boundary conditions on the lateral surfaces is studied on the basis of the linear theory of elasticity and linear electromechanical coupling. A discrete-continuous analytical numerical approach to solving the problems on wave propagation in piezoelectric ceramic hollow cylindrical bodies is proposed. A three-dimensional partial differential equation boundary value problem is reduced to a boundary value problem for a system of ordinary differential equations by representing the components of elastic tensors, displacement vectors, electric displacement, and electrostatic potential as waves traveling along the axial coordinate. The one-dimensional problem is solved by a stable method of discrete orthogonalization. The effect of electrical boundary conditions and the polarization direction of piezoceramics on the spectral characteristics of electroelastic wave propagation in a hollow piezoceramic homogeneous cylinder is analyzed. [ABSTRACT FROM AUTHOR]

A rotating semiconducting cylinder is studied within the framework of photo-thermoelasticity. The cylinder is exposed to an exponential pulse, acting as a variable heat flux. The study utilizes the Moore-Gibson-Thompson-Photo-Thermal equations of heat transfer. They incorporate two temperatures to describe the basic equations of the system. The Laplace transform is employed which allows for a more efficient and accurate solution. To calculate the displacement components, carrier density, thermal stresses, and conductive temperature in the physical domain, the numerical inversion techniques are utilized. Furthermore, MATLAB software is employed to generate graphical representations of all the parameters involved in the study. These visualizations illustrate the impact of thermal relaxations and various thermoelasticity theories that consider two temperatures. [ABSTRACT FROM AUTHOR]

A nonaxisymmetric contact problem on a circular interfacial inclusion of arbitrary shape under mixed boundary conditions with a piecewise homogeneous transversely isotropic space is considered. One edge of the inclusion is in smooth contact (tangential stresses are zero), while the other is in full contact with the medium. The problem is reduced to a system of five two-dimensional singular integral equations. For the inclusion, which has an axisymmetric shape under arbitrary loads, an exact solution of the system is obtained and its asymptotic properties are determined. On the basis of the latter, an efficient numerical-analytical method for solving the system of two-dimensional singular integral equations is proposed. The stress distribution in the vicinity of a coin-shaped inclusion is obtained and its features are revealed. [ABSTRACT FROM AUTHOR]

The novelty of the presented results is the deriving of exact solutions of axisymmetric poroelasticity problems for finite solid and hollow cylinders. The statement of these contact problems is given under the assumptions of Biot's model for poroelastic materials. A simulation of the poroelastic response of a cylinder is implemented using the apparatus of boundary problems. By the method of integral transforms, the original boundary problem is reduced to a one-dimensional boundary problem in the transform domain. Based on the exact solution of the latter one, it is manageable to derive the explicit formulas for displacements, stress, and pore pressure. The investigation of contact stress and pore pressure distribution inside the cylinder regarding its geometrical ratios, type of applied loading, and poroelastic material is carried out. [ABSTRACT FROM AUTHOR]

The parameters of a narrow small-scale plastic zone in an elastoplastic piece-wise homogeneous body undergoing a shear near the tip of an interfacial crack are calculated under plane strain conditions using the Wiener-Hopf method. Crack faces are in contact with friction. The plastic zone issuing out of the crack tip at an angle to a plane interface between media is modeled as the straight line of a displacement discontinuity involving two sections. Both tangential and normal displacements undergo the discontinuity at the section adjacent to the crack tip that models material destruction area. At the other section, only the tangential displacement experiences the discontinuity. The angle between the plastic zone and interface between the media is defined from the condition that the rate of energy dissipation in the zone is maximal. The sizes of the entire plastic zone, destruction zone and shear opening displacement of the crack in its tip are determined. It is studied how the friction of the crack faces, load, and the mechanical characteristics of the material influence on the parameters of the plastic zone and stress-strain state in the vicinity of the crack tip. [ABSTRACT FROM AUTHOR]

The reaction of a radial flexible ring with flanges in the supports of machine rotors to radial displacement has been studied. Two models of deformation and contact interaction of an elastic element with two rigid bodies positioned inside and outside of the ring have been developed. These models are based on variational statements with respect to the unknown forces and displacements. The options of gap and offset on both sides of the contact between the ring and the rigid bodies have been considered. A substantially nonlinear static reaction of the ring to radial displacement has been established. Radial reaction curves have been obtained across a wide range of design parameters, enabling a well-justified choice of an elastic damper with the desired stiffness properties. [ABSTRACT FROM AUTHOR]

A two-dimensional problem of the theory of elasticity is solved for a circular disk with an inclined edge crack, on a finite section of the boundary of which uniformly distributed pressure and tangential forces (friction forces) are applied. The contact load is balanced by concentrated forces and moment applied in the center of the disk. Contact with the friction of the crack faces is allowed. The problem is reduced to solving a system of two complex singular integral equations of the first kind with the Cauchy kernel. Numerical values of the stress intensity factors are obtained, depending on the location of the contact load on the disk boundary, as well as on the crack length and friction coefficients at the contact load application section and between the crack faces. The solution is presented using a railroad wheel as an example. [ABSTRACT FROM AUTHOR]

The problem of elastic and limiting equilibrium of a shallow spherical shell weakened by a pair of rectilinear cuts along the meridian is considered in a two-dimensional statement. One is considered to be a contact crack capable of closing, while the other one — a narrow slit with free faces. The contact interaction of the crack faces under bending load is described using a contact model along a line in the front surface of the shell. The numerical solution to the problem is developed by the method of singular integral equations using the mechanical quadrature algorithm. The regularities of the contact reaction distribution on the closed crack faces are studied. The effect of the shell curvature and the relative location of the defects on the values of intensity coefficients of forces and moments and on the value of the fracture load is studied. [ABSTRACT FROM AUTHOR]

The plane problem on the effect of a moving load on an incompressible half-plane with inhomogeneity in the form of a thin surface layer is considered. The effect of the moving load, initial stresses, and mechanical parameters of elements of a layered foundation on the main characteristics of its stress-strain state is studied. [ABSTRACT FROM AUTHOR]

A finite element formulation for the analysis of elastoplastic materials under finite strain levels, plane stress conditions, and mixed hardening is developed. The 3D hyperelastoplastic framework is condensed into a compact 2D form following the plane stress condition. The constitutive modeling accounts for the finite elastoplastic strains, associative plasticity, and mixed hardening. A kinematical approximation is based on the positional description and the isoparametric triangular membrane element of any order. Some examples are used to test the numerical formulation proposed. Several meshes are employed for each problem, varying the number of elements and approximation degree, which increases up to the fourth order. The results show that mesh refinement improves accuracy, avoiding locking problems and hourglass instabilities in plane stress problems involving large elastoplastic deformation, stress concentration, bending, mesh distortion, and post-buckling behavior. In addition to the convergence analysis regarding displacements and forces, some final values of the isotropic hardening parameter, the equivalent stress, and the backstress components are provided in order to assess the performance of all the element orders more completely. A comparison of the present results with finite element solutions from the scientific literature available is done, highlighting the similarities and differences for each problem. [ABSTRACT FROM AUTHOR]

The problem statement is given and the algorithm for solving problems of plasticity for axisymmetric bodies made of isotropic materials with properties depending on a stress mode and plastic loosening is described. The constitutive equations of the theory of deformation processes along the trajectories of small curvature containing two nonlinear dependences are used. One of them implements the relationship between the first invariants of stress and strain tensors, and the other one implements the relationship between the second invariants of the corresponding deviators. The effect of the dependence of deformation curves on the stress mode and the plastic change in the bulk strain on the results of calculating the stress-strain state of the shell is studied. [ABSTRACT FROM AUTHOR]

The problem of the compression of two electroelastic transversely isotropic half-spaces having different properties with a rigid flat inclusion of arbitrary shape between them is studied. When considering the problem, it is assumed that the surfaces of the half-spaces do not have electrode coatings. The regularities of contact interaction of two piezoelectric transversely isotropic half-spaces (with nonelectroded surfaces) with a flat inclusion of arbitrary shape under compression are determined on the basis of representation of the general solution of the system of static equations of electroelasticity for a transversely isotropic piezoelectric body using harmonic functions. A generalization of Gladwell's result on the contact interaction of two isotropic elastic half-spaces with a rigid flat inclusion of arbitrary shape under compression is obtained for the case of interaction with an inclusion of two electroelastic transversely isotropic half-spaces. For a disk-shaped inclusion (the partial case of the problem), numerical studies have been carried out, and the effect of the electroelastic properties of half-spaces and the geometric dimensions of the inclusion on the parameters of contact interaction has been studied. [ABSTRACT FROM AUTHOR]

The first basic plane stress state problem of the equilibrium of a nonlinear orthotropic body with a mode I intrinsic crack is stated in the terms of displacement vector components. It is supposed that there is a fracture process zone at the vicinity of each crack tip. In deriving invariant equations, the model of the fracture process zone in form of an open slit with a stress vector on its surfaces was used. The state of the fracture process zone is described by equations including a scalar function with two constants. The solution of the boundary-value problem has shown that the single non-zero component of the stress vector at points on the body surfaces, specific fracture energy as well as the single non-zero component of the stress vector at points on the slit surfaces, and the slit opening depend on the above constants. It is established that these constants affect the shape of the nonlinearity zone adjacent to each crack tip. An experimental-theoretical method to determine the constants is proposed. [ABSTRACT FROM AUTHOR]

Numerical modeling of the coupled processes of deformation of the coal massif with s mine working and gas filtration in the disturbed area was carried out. The modeling takes into account changes in rock permeability depending on their stress state. Cases of a frame supported or roof bolted working are considered. Inelastic strain zones, distributions of stress fields, strains, permeability coefficients, and gas pressure are determined. Curves of changes in geomechanical and filtration parameters over time are presented. The results are analyzed. It is shown that roof bolting can be used not only to maintain the stable state of mine workings but also as a technological means of reducing methane emissions into the mine atmosphere. [ABSTRACT FROM AUTHOR]

The article is devoted to the life and work of the world-famous scientist and engineer, outstanding organizer of science and educator, one of the founders of the Ukrainian Academy of Sciences, founder, director, and organizer of the first technical institute in Ukraine, S. P. Timoshenko. The main attention is paid to his contribution to the development of research in the field of mechanics in Ukraine, the creation of the first scientific institutions of the Academy, and the organization of training of scientific and teaching staff. S. P. Timoshenko's main scientific achievements are also described, and his contribution to the development of engineering education is highlighted. [ABSTRACT FROM AUTHOR]

The problem of reducing the effect of the mobility of free surface fluid on the motion of the carrying structure is considered. For the mathematical description of the problem, a variational approach with elements of nonlinear mechanics and ideas of the method of modal decomposition of system variables is used. This approach makes it possible to determine, in an analytical form, the internal forces of interaction of the fluid with the tank walls. The proposed control method is based on the idea of compensating the interaction of the fluid with the structure by including this force in the special control. This approach is tested against various control problems (for short-term and harmonic perturbations). The capabilities of the method are tested using different approximate determinations of the force reaction of the fluid. The results show that in the case of a simplified (linear) or single-term determination of the force reaction of the fluid, this method gives significant errors at the initial stage of motion, but later these deviations decrease substantially and, as a result, the effect of fluid mobility on the carrying structure is practically eliminated. [ABSTRACT FROM AUTHOR]

A unified approach to the analysis of the nonstationary vibrations of piezoelectric ceramic plane layers, cylinders, and spheres taking into account the functional inhomogeneity and viscoelasticity of the material is proposed. The standard model of vibration damping and the Kelvin–Voigt viscoelastic model are considered. The proposed approach makes it possible to study the transition of the transducer to a static state or to a steady-state vibration mode under nonstationary perturbations. The effect of functional inhomogeneity on the nonstationary vibrations of a piezoelectric element is analyzed. The damping of the vibrations and viscoelastic axisymmetric vibrations of a radially polarized cylinder under electrical and mechanical perturbation using the Heaviside function is calculated. The dynamics of damping is analyzed, and the obtained results are compared with the static solution to validate the results. The generation of voltage by a piezoceramic cylinder under mechanical axisymmetric loading is also studied taking into account the viscoelastic properties of the material. It was found that the time to reach the steady-state mode for mechanical and electrical loads is almost the same. [ABSTRACT FROM AUTHOR]

The Lyapunov direct method is generalized to dynamic equations with conformable fractional derivative of the state vector. New estimates of the change of Lyapunov functions along the solutions of conformable fractional equations based on integral inequalities on time scale are established. These estimates are used to analyze various types of stability and boundedness of the solutions of dynamic equations with conformable fractional derivative of the state vector. [ABSTRACT FROM AUTHOR]

Torsional waves as one of the types of nonlinear elastic cylindrical displacement waves are analyzed theoretically within the framework of the five-constant Murnaghan model. The analysis is based on tools of the nonlinear theory of elasticity. Two variants of new nonlinear wave equations for torsional waves are derived taking into account cubicallyt nonlinear terms. The difference between the variants is in the different ways of allowing for the nonlinearities in the wave equation. The simpler variant is considered, and the evolution of torsional waves is analyzed theoretically and numerically. Special attention is paid to the boundary conditions and the transcendent equation classical for torsional waves. [ABSTRACT FROM AUTHOR]