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Vol 89, No 4 (2025)
Articles
Ricci tensor in the problem on thermoelastic stresses
Abstract
The paper is devoted to the interrelations between stresses, temperature change field, and the Ricci tensor in problems of linear thermoelasticity. A new model of thermoelastic states is proposed. It is demonstrated that inelastic (thermoelastic) behavior is due to the Ricci tensor, which is in turn determined by the temperature field inhomogeneities. The classical linear thermoelastic models can be treated as a special case of the proposed model while the specific assumptions concerning the strain tensor are applied.
533-545
Energy supply into a semi-infinite β — fermi-pasta-ulam-tsingou chain by periodic kinematic loading
Abstract
Energy supply into a semi-infinite one-dimensional Fermi-Pasta-Ulam-Tsingou (FPUT) crystal (chain) at a boundary subjected to sinusoidal kinematic loading is examined. It is demonstrated that, in the linear approximation, the energy input problem can be considered symmetric with respect to the boundary for all loading frequencies. Utilizing the renormalized dispersion relation for the chain, an asymptotic approximation for the input energy at large times is derived. It is shown that at low and moderate frequencies, the obtained estimate of the total energy aligns with the results of numerical simulations, whereas a divergence is observed at high loading frequencies.
546-558
Eigenoscillations of the junction of an elastic body and thin rods
Abstract
We study behaviour of eigenfrequencies of an anisotropic and homogeneous body with several thin cylindrical elastic rods whose exterior ends are clamped. We prove that, as rods thin, in the low-frequency range limits of normalized eigenvalues of the singularly perturbed elasticity problem imply eigenvalues of the family of systems of ordinary differential equations on rod’s axes with the Dirichlet and the Steklov boundary conditions at the outer and inner endpoints respectively while the systems are combined into a joint spectral problem by these the Steklov conditions. For an isotropic junction the limiting problem decouples into the Dirichlet problem for fourth order differential operators and the algebraic problem for a symmetric positive matrix of a size dependent on the number of clamped rods.
559-587
Magnetomechanics of a graphene sheet. Theory and solution of an applied problem
Abstract
Interest in graphene is due to a wide range of unique physical and mechanical properties: high Young's modulus, high shear modulus, high strength, etc., as well as high electrical and thermal conductivity. From this point of view, the study of the deformation properties of graphene is one of the most actual branches of modern nanomechanics of materials and structural members (nanodevices). The application of mechanics to the study of nanomaterials, in particular, two-dimensional nanomaterials (graphene, carbon nanotube) is aimed at creating and developing a continuum theory of deformation behavior and having based on this theory, studying a number of applied problems. The moment-membrane theory of elastic thin plates and shells gives an adequate continuum theory of the mechanical behavior of a graphene sheet and a single-layered carbon nanotube (which is constructed taking account of the natural modeling of interactions between atoms in their crystal lattices, i.e. considering this interaction as both force and moment). It is known that due to their unique electrical and mechanical properties, both graphene and carbon nanotube are can be treated as supersensitive elements in the creation of nanoelectromechanical systems. On this basis, it is actual to develop a magnetomechanical theory of the dynamic behavior of a graphene sheet (as well as a carbon nanotube) placed in a given homogeneous magnetic field. In this paper, based on the equations of three-dimensional magnetoelasticity as a moment theory of elasticity with independent fields of displacements and rotations, by using hypotheses concerning the characteristics of mechanical behavior and the characteristics of the behavior of the electromagnetic field in thin regions, a two-dimensional model of magnetoelasticity is proposed according to the moment-membrane theory of elastic plates, which then is applied to a modeling magnetoelastic dynamics of a graphene sheet. Based on the proposed model of magnetoelastic dynamics of a graphene sheet, a problem of free one-dimensional bending oscillations of a two-dimensional body placed in a given homogeneous magnetic field is considered. Analyzing the obtained numerical results, it is shown that magnetoelastic oscillations have a damping nature, the behavior of both the oscillation frequency and the oscillation damping parameter are established depending on the values of the induction of a given magnetic field. Based on these results, a possible range of application of a graphene sheet to a nanoelectromechanical resonator is discussed.
588-609
Contact problem for an orthotropic layer with an undetermined contact zone
Abstract
The spatial contact problem related to indenting one/two asymmetrical rigid solids into an orthotropic layer is considered. The opposite surface of the layer lies on a rigid base (friction effects of the interface are neglected). The problem is reduced to an integral equation with the kernel the principal part of which can be separated and does not contain inner integration. This part corresponds to the case of indentation into an orthotropic half-space. Under conditions of an undetermined contact area, a numerical method for nonlinear boundary integral equations is used to simultaneously determine the contact area and the contact pressure. Mechanical characteristics of the contact behavior are studied. The effect of initially discrete contact areas confluxtion for a pair of indentors located along a chosen direction is discussed.
610-617
Distinctive features of moment shells theory using for calculation of hyperelastic cylindrical shells inflation
Abstract
The paper concerns investigation of nonlinear moment shells theories equations application to solution of axisymmetric hyperelastic cylindrical shell static inflation problems. Elasticity equations used for calculation of shells deforming at arbitrary displacements and rotations and relations are obtained on the basis of a modified Kirchhoff–Love model. Results of calculations of linear elastic and neo-Hookean cylindrical shell based on moment theories relations and traditionally used for considered problems solution momentless theory are compared. Shell thickness is considered to be both constant and variable. It is shown that moment theories equations are suitable only when stress-strain state rapidly varying along a meridian. These equations possess a well-posedeness in comparison to equations of shells theory based on the modified Kirchhoff–Love model.
618-627
Identification of filtration-capacity parameters of non-newtonian oil reservoirs whose rocks subjected to irreversible deformation
Abstract
A method of identification of filtration-capacity parameters of non-Newtonian oil reservoirs, the rocks of which are subjected to irreversible deformations, is proposed. By the aid of this methodology, taking into account the rheology of rocks and using the data of exploitation history, calculations can be realized on order to determine the filtration-capacity parameters of the reservoir of non-Newtonian oil.
628-634
Methods of terrestrial seismic protection of on-, under-ground structures and tunnels. A review
Abstract
This paper briefly presents an overview of previous studies that are relevant to the current research. Background information is provided. This includes some basic knowledge of ground vibrations, ground vibration reduction techniques, the use of wave barrier for vibration isolation, responses of existing tunnels under near-burst, and mitigation measures to reduce tunnel vibration.
635-672